1.5: Capítulo 1 Ejercicios con soluciones

En los Ejercicios ( PageIndex {1} ) – ( PageIndex {8} ), encuentre la factorización prima del número natural dado.

Ejercicio ( PageIndex {1} )

Respuesta: (80 = 2 cdot 2 cdot 2 cdot 2 cdot 5 )

Ejercicio ( PageIndex {2} )

108

Ejercicio ( PageIndex {3} )

180

Respuesta: (180 = 2 cdot 2 cdot 3 cdot 3 cdot 5 )

Ejercicio ( PageIndex {4} )

160

Ejercicio ( PageIndex {5} )

128

Respuesta: (128 = 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 )

Ejercicio ( PageIndex {6} )

192

Ejercicio ( PageIndex {7} )

Respuesta: (32 = 2 cdot 2 cdot 2 cdot 2 cdot 2 )

Ejercicio ( PageIndex {8} )

En los Ejercicios ( PageIndex {9} ) – ( PageIndex {16} ), convierte el decimal dado en una fracción.

Ejercicio ( PageIndex {9} )

0,648

Respuesta: Hay tres lugares decimales, entonces (0.648 = frac {648} {1000} = frac {81} {125} )

Ejercicio ( PageIndex {10} )

0,62

Ejercicio ( PageIndex {11} )

0.240

Respuesta: Hay tres lugares decimales, entonces (0.240 = frac {240} {1000} = frac {6} {25} )

Ejercicio ( PageIndex {12} )

0,90

Ejercicio ( PageIndex {13} )

0,14

Respuesta: Hay dos lugares decimales, entonces (0.14 = frac {14} {100} = frac {7} {50} )

Ejercicio ( PageIndex {14} )

0,760

Ejercicio ( PageIndex {15} )

0,888

Respuesta: Hay tres lugares decimales, entonces (0.888 = frac {888} {1000} = frac {111} {125} )

Ejercicio ( PageIndex {16} )

0,104

En los Ejercicios ( PageIndex {17} ) – ( PageIndex {24} ), convierte el decimal repetido dado en una fracción.

Ejercicio ( PageIndex {17} )

(0. Overline {27} )

Respuesta

Sea (x = 0. Overline {27}. ) Entonces (100 x = 27. Overline {27}. ) Restando a ambos lados de estas ecuaciones.

[ begin {alineado} 100 x & = 27. overline {27} \ x & = 0. overline {27} end {alineado} ]

produce (99 x = 27. ) Finalmente, resuelva (x ) dividiendo por (99: x = frac {27} {99} = frac {3} {11} ) .

Ejercicio ( PageIndex {18} )

(0. Overline {171} )

Ejercicio ( PageIndex {19} )

(0. Overline {24} )

Respuesta

Sea (x = 0. Overline {24}. ) Entonces (100 x = 24. Overline {24}. ) Restando a ambos lados de estas ecuaciones [ begin {alineado} 100 x & = 24. overline {24} \ x & = 0. overline {24} end {alineado} ]

produce (99 x = 24. ) Finalmente, resuelva (x ) dividiendo por (99: x = frac {24} {99} = frac {8} {33} )

Ejercicio ( PageIndex {20} )

(0. Overline {882} )

Ejercicio ( PageIndex {21} )

(0. Overline {84} )

Respuesta

Sea (x = 0. Overline {84}. ) Entonces (100 x = 84. Overline {84}. ) Restando a ambos lados de estas ecuaciones

[ begin {alineado} 100 x & = 84. overline {.84} \ x & = 0. overline {84} end {alineado} ]

produce (99 x = 84. ) Finalmente, resuelva (x ) dividiendo por (99: x = frac {84} {99} = frac {28} {33} )

Ejercicio ( PageIndex {22} )

(0. Overline {384} )

Ejercicio ( PageIndex {23} )

(0. Overline {63} )

Respuesta

Sea (x = 0. Overline {63}. ) Entonces (100 x = 63. Overline {63}. ) Restando a ambos lados de estas ecuaciones

[ begin {alineado} 100 x & = 63. overline {63} \ x & = 0. overline {63} end {alineado} ]

produce (99 x = 63. ) Finalmente, resuelva (x ) dividiendo por (99: x = frac {63} {99} = frac {7} {11} )

Ejercicio ( PageIndex {24} )

(0. Overline {60} )

Ejercicio ( PageIndex {25} )

Demuestre que ( sqrt {3} ) es irracional.

Respuesta

Suponga que ( sqrt {3} ) es racional. Entonces se puede expresar como la razón de dos enteros p y q de la siguiente manera:

[ sqrt {3} = frac {p} {q} ]

Cuadrado de ambos lados, [3 = frac {p ^ {2}} {q ^ {2}} ]

luego borra la ecuación de fracciones multiplicando ambos lados por (q ^ {2} ):

[p ^ {2} = 3 q ^ {2} ]

Ahora pyq tienen sus propias factorizaciones primarias únicas. Tanto (p ^ {2} ) como (q ^ {2} ) tienen un número par de factores en sus factorizaciones primas. Pero esto contradice la ecuación (1), porque el lado izquierdo tendría un número par de factores en su factorización prima, mientras que el lado derecho tendría un número impar de factores en su factorización prima (hay un 3 extra en el lado derecho).

Por lo tanto, nuestra suposición de que ( sqrt {3} ) era racional es falsa. Por lo tanto, ( sqrt {3} ) es irracional.

Ejercicio ( PageIndex {26} )

Demuestre que ( sqrt {5} ) es irracional.

En los Ejercicios ( PageIndex {27} ) – ( PageIndex {30} ), copie la tabla dada en su tarea. En cada fila, coloque una marca de verificación en cada columna que sea apropiada. Es decir, si el número al comienzo de la fila es racional, coloque una marca de verificación en la columna racional. Nota: La mayoría de las filas (pero no todas) tendrán más de una marca de verificación.

Ejercicio ( PageIndex {27} )

	( mathbb {N} )	( mathbb {W} )	( mathbb {Z} )	( mathbb {Q} )	( mathbb {R} )
0
-2
-2/3
0,15
(0. Overline {2} )
( sqrt {5} )

Respuesta

	( mathbb {N} )	( mathbb {W} )	( mathbb {Z} )	( mathbb {Q} )	( mathbb {R} )
0		x	x	x	x
-2			x	x	x
-2/3				x	x
0,15				x	x
(0. Overline {2} )				x	x
( sqrt {5} )					x

Ejercicio ( PageIndex {28} )

	( mathbb {N} )	( mathbb {W} )	( mathbb {Z} )	( mathbb {Q} )	( mathbb {R} )
10/2
( pi )
-6
(0. Overline {9} )
( sqrt {2} )
0,37

Ejercicio ( PageIndex {29} )

	( mathbb {N} )	( mathbb {W} )	( mathbb {Z} )	( mathbb {Q} )	( mathbb {R} )
-4/3
12
0
( sqrt {11} )
(1. Overline {3} )
6/2

Respuesta

	( mathbb {N} )	( mathbb {W} )	( mathbb {Z} )	( mathbb {Q} )	( mathbb {R} )
-4/3				x	x
12	x	x	x	x	x
0		x	x	x	x
( sqrt {11} )					x
(1. Overline {3} )				x	x
6/2	x	x	x	x	x

Ejercicio ( PageIndex {30} )

	( mathbb {N} )	( mathbb {W} )	( mathbb {Z} )	( mathbb {Q} )	( mathbb {R} )
-3/5
( sqrt {10} )
1,625
10/2
0/5
11

En los Ejercicios ( PageIndex {31} ) – ( PageIndex {42} ), considere la declaración dada y determine si es verdadera o falsa. Escribe una oración explicando tu respuesta. En particular, si la declaración es falsa, intente dar un ejemplo que contradiga la declaración.

Ejercicio ( PageIndex {31} )

Todos los números naturales son números enteros.

Respuesta: Cierto. La única diferencia entre los dos conjuntos es que el conjunto de números enteros contiene el número 0.

Ejercicio ( PageIndex {32} )

Todos los números enteros son números racionales.

Ejercicio ( PageIndex {33} )

Todos los números racionales son enteros.

Respuesta: Falso. Por ejemplo, ( frac {1} {2} ) no es un número entero.

Ejercicio ( PageIndex {34} )

Todos los números racionales son números enteros.

Ejercicio ( PageIndex {35} )

Algunos números naturales son irracionales.

Respuesta: Falso. Todos los números naturales son racionales y, por lo tanto, no irracionales.

Ejercicio ( PageIndex {36} )

Algunos números enteros son irracionales.

Ejercicio ( PageIndex {37} )

Algunos números reales son irracionales.

Respuesta: Cierto. Por ejemplo, π y √2 son números reales que son irracionales.

Ejercicio ( PageIndex {38} )

Todos los enteros son números reales.

Ejercicio ( PageIndex {39} )

Todos los enteros son números racionales.

Respuesta: Cierto. Cada entero b se puede escribir como una fracción b / 1.

Ejercicio ( PageIndex {40} )

No hay números racionales son números naturales.

Ejercicio ( PageIndex {41} )

No hay números reales son enteros.

Respuesta: Falso. Por ejemplo, 2 es un número real que también es un número entero.

Ejercicio ( PageIndex {42} )

Todos los números enteros son números naturales.

En los Ejercicios ( PageIndex {43} ) – ( PageIndex {54} ), resuelve cada una de las ecuaciones dadas para x.

Ejercicio ( PageIndex {43} )

45x + 12 = 0

Respuesta: [ begin {alineado} & 45 x + 12 = 0 \ Longrightarrow quad & 45 x = -12 \ Longrightarrow quad & x = – frac {12} {45} = – frac {4} {15} end {alineado} ]

Ejercicio ( PageIndex {44} )

76x – 55 = 0

Ejercicio ( PageIndex {45} )

x – 7 = −6x + 4

Respuesta: [ begin {alineado} & x-7 = -6 x + 4 \ Longrightarrow quad & x + 6 x = 4 + 7 \ Longrightarrow quad & 7 x = 11 \ Longrightarrow quad & x = frac {11} {7} end {alineado} ]

Ejercicio ( PageIndex {46} )

−26x + 84 = 48

Ejercicio ( PageIndex {47} )

37x + 39 = 0

Respuesta: [ begin {alineado} & 37 x + 39 = 0 \ Longrightarrow quad & 37 x = -39 \ Longrightarrow quad & x = – frac {39} {37} end { alineado} ]

Ejercicio ( PageIndex {48} )

−48x + 95 = 0

Ejercicio ( PageIndex {49} )

74x – 6 = 91

Respuesta: [ begin {alineado} & 74 x-6 = 91 \ Longrightarrow quad & 74 x = 97 \ Longrightarrow quad & x = frac {97} {74} end {alineado} ]

Ejercicio ( PageIndex {50} )

−7x + 4 = −6

Ejercicio ( PageIndex {51} )

−88x + 13 = −21

Respuesta: [ begin {alineado} & -88 x + 13 = -21 \ Longrightarrow quad & -88 x = -34 \ Longrightarrow quad & x = frac {-34} {- 88 } = frac {17} {44} end {alineado} ]

Ejercicio ( PageIndex {52} )

−14x – 81 = 0

Ejercicio ( PageIndex {53} )

19x + 35 = 10

Respuesta: [ begin {alineado} & 19 x + 35 = 10 \ Longrightarrow quad & 19 x = -25 \ Longrightarrow quad & x = – frac {25} {19} end { alineado} ]

Ejercicio ( PageIndex {54} )

−2x + 3 = −5x – 2

En los Ejercicios ( PageIndex {55} ) – ( PageIndex {66} ), resuelve cada una de las ecuaciones dadas para x.

Ejercicio ( PageIndex {55} )

6 – 3 (x + 1) = −4 (x + 6) + 2

Respuesta: [ begin {alineado} y 6-3 (x + 1) = – 4 (x + 6) +2 \ Longrightarrow quad y 6-3 x-3 = -4 x-24 + 2 \ Longrightarrow quad & -3 x + 3 = -4 x-22 \ Longrightarrow quad & -3 x + 4 x = -22-3 \ Longrightarrow quad & x = -25 end { alineado} ]

Ejercicio ( PageIndex {56} )

(8x + 3) – (2x + 6) = −5x + 8

Ejercicio ( PageIndex {57} )

−7 – (5x – 3) = 4 (7x + 2)

[ begin {alineado} & -7- (5 x-3) = 4 (7 x + 2) \ Longrightarrow quad & -7-5 x + 3 = 28 x + 8 \ Longrightarrow quad & -5 x-4 = 28 x + 8 \ Longrightarrow quad & -5 x-28 x = 8 + 4 \ Longrightarrow quad & -33 x = 12 \ Longrightarrow quad & x = – frac {12} {33} = – frac {4} {11} end {alineado} ]

Ejercicio ( PageIndex {58} )

−3-4 (x + 1) = 2 (x + 4) + 8

Ejercicio ( PageIndex {59} )

9 – (6x – 8) = −8 (6x – 8)

Respuesta: [ begin {alineado} y 9- (6 x-8) = – 8 (6 x-8) \ Longrightarrow quad y 9-6 x + 8 = -48 x + 64 \ Longrightarrow quad & -6 x + 17 = -48 x + 64 \ Longrightarrow quad & -6 x + 48 x = 64-17 \ Longrightarrow quad & 42 x = 47 \ Longrightarrow quad & x = frac {47} {42} end {alineado} ]

Ejercicio ( PageIndex {60} )

−9 – (7x – 9) = −2 (−3x + 1)

Ejercicio ( PageIndex {61} )

(3x – 1) – (7x – 9) = −2x – 6

Respuesta: [ begin {alineado} & (3 x-1) – (7 x-9) = – 2 x-6 \ Longrightarrow quad & 3 x-1-7 x + 9 = -2 x -6 \ Longrightarrow quad & -4 x + 8 = -2 x-6 \ Longrightarrow quad & -4 x + 2 x = -6-8 \ Longrightarrow quad & -2 x = – 14 \ Longrightarrow quad & x = 7 end {alineado} ]

Ejercicio ( PageIndex {62} )

−8-8 (x – 3) = 5 (x + 9) + 7

Ejercicio ( PageIndex {63} )

(7x – 9) – (9x + 4) = −3x + 2

Respuesta: [ begin {alineado} & (7 x-9) – (9 x + 4) = – 3 x + 2 \ Longrightarrow quad y 7 x-9-9 x-4 = -3 x +2 \ Longrightarrow quad & -2 x-13 = -3 x + 2 \ Longrightarrow quad & -2 x + 3 x = 2 + 13 \ Longrightarrow quad & x = 15 end { alineado} ]

Ejercicio ( PageIndex {64} )

(−4x – 6) + (−9x + 5) = 0

Ejercicio ( PageIndex {65} )

−5 – (9x + 4) = 8 (−7x – 7)

Respuesta: [ begin {array} {ll} {} & {-5- (9 x + 4) = 8 (-7 x-7)} \ { Longrightarrow} & {-5-9 x- 4 = -56 x-56} \ { Longrightarrow} & {-9 x-9 = -56 x-56} \ { Longrightarrow} & {-9 x + 56 x = -56 + 9} \ { Longrightarrow} & {47 x = -47} \ { Longrightarrow} & {x = -1} end {array} ]

Ejercicio ( PageIndex {66} )

(8x – 3) + (−3x + 9) = −4x – 7

En los Ejercicios ( PageIndex {67} ) – ( PageIndex {78} ), resuelve cada una de las ecuaciones dadas para x. Verifique sus soluciones usando su calculadora.

Ejercicio ( PageIndex {67} )

−3,7x – 1 = 8,2x – 5

Respuesta

Primeros decimales claros al multiplicar por 10.

[ begin {alineado} & -3.7 x-1 = 8.2 x-5 \ Longrightarrow quad & -37 x-10 = 82 x-50 \ Longrightarrow quad & -37 x-82 x = -50 + 10 \ Longrightarrow quad & -119 x = -40 \ Longrightarrow quad & x = frac {40} {119} end {alineado} ]

Aquí hay una comprobación de las soluciones en la calculadora gráfica. El lado izquierdo de la ecuación se evalúa en la solución en (a), el lado derecho de la ecuación se evalúa en la solución en (b). Tenga en cuenta que coinciden.

$Screen Shot 2019-07-26 at 3.54.32 PM.png$

Ejercicio ( PageIndex {68} )

8.48x – 2.6 = −7.17x – 7.1

Ejercicio ( PageIndex {69} )

(- frac {2} {3} x + 8 = frac {4} {5} x + 4 )

Respuesta

Primeras fracciones claras multiplicando por 15.

[ begin {alineado} & – frac {2} {3} x + 8 = frac {4} {5} x + 4 \ Longrightarrow quad & -10 x + 120 = 12 x +60 \ Longrightarrow quad & -10 x-12 x = 60-120 \ Longrightarrow quad & -22 x = -60 \ Longrightarrow quad & x = frac {-60} {- 22 } = frac {30} {11} end {alineado} ]

$Screen Shot 2019-07-26 at 4.00.59 PM.png$

Ejercicio ( PageIndex {70} )

−8.4x = −4.8x + 2

Ejercicio ( PageIndex {71} )

(- frac {3} {2} x + 9 = frac {1} {4} x + 7 )

Respuesta

Primeras fracciones claras multiplicando por 4.

[ begin {alineado} & – frac {3} {2} x + 9 = frac {1} {4} x + 7 \ Longrightarrow quad & -6 x + 36 = x + 28 \ Longrightarrow quad & -6 xx = 28-36 \ Longrightarrow quad & -7 x = -8 \ Longrightarrow quad & x = frac {8} {7} end {alineado} ]

$Screen Shot 2019-07-26 at 4.02.24 PM.png$

Ejercicio ( PageIndex {72} )

2.9x – 4 = 0.3x – 8

Ejercicio ( PageIndex {73} )

5.45x + 4.4 = 1.12x + 1.6

Respuesta

Primeros decimales claros al multiplicar por 100.

[ begin {alineado} & 5.45 x + 4.4 = 1.12 x + 1.6 \ Longrightarrow quad & 545 x + 440 = 112 x + 160 \ Longrightarrow quad & 545 x-112 x = 160 -440 \ Longrightarrow quad & 433 x = -280 \ Longrightarrow quad & x = – frac {280} {433} end {alineado} ]

$Screen Shot 2019-07-26 at 4.03.55 PM.png$

Ejercicio ( PageIndex {74} )

(- frac {1} {4} x + 5 = – frac {4} {5} x-4 )

Ejercicio ( PageIndex {75} )

(- frac {3} {2} x-8 = frac {2} {5} x-2 )

Respuesta

Primeras fracciones claras al multiplicar por 10. [ begin {alineado} & – frac {3} {2} x-8 = frac {2} {5} x-2 \ Longrightarrow quad & -15 x-80 = 4 x-20 \ Longrightarrow quad & -15 x-4 x = -20 + 80 \ Longrightarrow quad & -19 x = 60 \ Longrightarrow quad & x = – frac {60} {19} end {alineado} ]

$Screen Shot 2019-07-26 at 4.06.54 PM.png$

Ejercicio ( PageIndex {76} )

(- frac {4} {3} x-8 = – frac {1} {4} x + 5 )

Ejercicio ( PageIndex {77} )

−4.34x – 5.3 = 5.45x – 8.1

Respuesta

Primeros decimales claros al multiplicar por 100.

[ begin {alineado} & -4.34 x-5.3 = 5.45 x-8.1 \ Longrightarrow quad & -434 x-530 = 545 x-810 \ Longrightarrow quad & -434 x-545 x = -810 + 530 \ Longrightarrow quad & -979 x = -280 \ Longrightarrow quad & x = frac {280} {979} end {alineado} ]

$Screen Shot 2019-07-26 at 4.11.18 PM.png$

Ejercicio ( PageIndex {78} )

( frac {2} {3} x-3 = – frac {1} {4} x-1 )

En los Ejercicios ( PageIndex {79} ) – 50, resuelva cada una de las ecuaciones dadas para la variable indicada.

Ejercicio ( PageIndex {79} )

P = IRT para R

Respuesta: [ begin {alineado} & P = IRT \ Longrightarrow quad & P = (IT) R \ Longrightarrow quad & frac {P} {IT} = frac {(IT) R } {IT} \ Longrightarrow quad & frac {P} {IT} = R end {alineado} ]

Ejercicio ( PageIndex {80} )

d = vt para t

Ejercicio ( PageIndex {81} )

(v = v_ {0} + a t ) para (a )

Respuesta: [ begin {alineado} & v = v_ {0} + en \ Longrightarrow quad & v-v_ {0} = en \ Longrightarrow quad & frac {v-v_ {0} } {t} = a end {alineado} ]

Ejercicio ( PageIndex {82} )

(x = v_ {0} + v t ) para (v )

Ejercicio ( PageIndex {83} )

Ax + By = C para y

Respuesta: [ begin {alineado} & A x + B y = C \ Longrightarrow quad & B y = CA x \ Longrightarrow quad & y = frac {CA x} {B} end {alineado} ]

Ejercicio ( PageIndex {84} )

y = mx + b para x

Ejercicio ( PageIndex {85} )

(A = pi r ^ {2} ) para ( pi )

Respuesta: [ begin {alineado} A & = pi r ^ {2} \ Longrightarrow quad frac {A} {r ^ {2}} & = pi end {alineado} ] [ 19459002]

Ejercicio ( PageIndex {86} )

(S = 2 pi r ^ {2} +2 pi r h ) para (h )

Ejercicio ( PageIndex {87} )

(F = frac {k q q_ {0}} {r ^ {2}} ) para (k )

Respuesta: [ begin {alineado} & F = frac {kq q_ {0}} {r ^ {2}} \ Longrightarrow quad & F r ^ {2} = kq q_ {0} \ Longrightarrow quad & frac {F r ^ {2}} {q q_ {0}} = k end {alineado} ]

Ejercicio ( PageIndex {88} )

(C = frac {Q} {m T} ) para (T )

Ejercicio ( PageIndex {89} )

( frac {V} {t} = k ) para (t )

Respuesta: [ begin {alineado} & frac {V} {t} = k \ Longrightarrow quad & V = kt \ Longrightarrow quad & frac {V} {k} = t end {alineado} ]

Ejercicio ( PageIndex {90} )

( lambda = frac {h} {m v} ) para (v )

Ejercicio ( PageIndex {91} )

( frac {P_ {1} V_ {1}} {n_ {1} T_ {1}} = frac {P_ {2} V_ {2}} {n_ {2} T_ {2}} ) para (V_ {2} )

Respuesta

Multiplica en cruz, luego divide por el coeficiente de (V_ {2} ).

[ begin {alineado} & frac {P_ {1} V_ {1}} {n_ {1} T_ {1}} = frac {P_ {2} V_ {2}} {n_ {2 } T_ {2}} \ Longrightarrow quad & n_ {2} P_ {1} V_ {1} T_ {2} = n_ {1} P_ {2} V_ {2} T_ {1} \ Longrightarrow quad & frac {n_ {2} P_ {1} V_ {1} T_ {2}} {n_ {1} P_ {2} T_ {1}} = V_ {2} end {alineado} ] [ 19459002]

Ejercicio ( PageIndex {92} )

( pi = frac {n R T} {V} i ) para (n )

Ejercicio ( PageIndex {93} )

Ate una pelota a una cuerda y gírela en un círculo con velocidad constante. Se sabe que la aceleración de la pelota es directamente hacia el centro del círculo y viene dada por la fórmula [a = frac {v ^ {2}} {r} ] donde a es aceleración, v es la velocidad de la pelota, y r es el radio del círculo de movimiento.

i. Resuelve la fórmula (1) para r.

ii. Dado que la aceleración de la pelota es de 12 m / s2 y la velocidad es de 8 m / s, encuentre el radio del círculo de movimiento.

Respuesta

Multiplica en cruz, luego divide por el coeficiente de r.

[ begin {alineado} a & = frac {v ^ {2}} {r} \ ar & = v ^ {2} \ r & = frac {v ^ {2}} { a} end {alineado} ]

Para encontrar el radio, sustituya la aceleración (a = 12 mathrm {m} / mathrm {s} ^ {2} ) y la velocidad v = 8 m / s.

[r = frac {v ^ {2}} {a} = frac {(8) ^ {2}} {12} = frac {64} {12} = frac {16} { 3} ]

Por lo tanto, el radio es (r = 16/3 mathrm {m}, ) o 5 ( frac {1} {3} ) metros.

Ejercicio ( PageIndex {94} )

Una partícula se mueve a lo largo de una línea con aceleración constante. Se sabe que la velocidad de la partícula, en función de la cantidad de tiempo que ha pasado, viene dada por la ecuación

[v = v_ {0} + a t ] donde v es la velocidad en el tiempo t, v0 es la velocidad inicial de la partícula (en el tiempo t = 0), y a es la aceleración de la partícula.

i. Resuelve la fórmula (2) para t.

ii. Sabes que la velocidad actual de la partícula es 120 m / s. También sabe que la velocidad inicial fue de 40 m / sy la aceleración ha sido constante (a = 2 mathrm {m} / mathrm {s} ^ {2} ). ¿Cuánto tiempo le tomó a la partícula alcanzar su velocidad actual?

Ejercicio ( PageIndex {95} )

Al igual que la Ley Universal de Gravitación de Newton, la fuerza de atracción (repulsión) entre dos partículas cargadas diferentes (como) es proporcional al producto de las cargas e inversamente proporcional a la distancia entre ellas. [F = k_ {C} frac {q_ {1} q_ {2}} {r ^ {2}} ] En esta fórmula, (k_ {C} aprox 8.988 veces 10 ^ {9} mathrm {Nm} ^ {2} / mathrm {C} ^ {2} ) y se llama constante electrostática. Las variables q1 y q2 representan las cargas (en Coulombs) en las partículas (que podrían ser números positivos o negativos) yr representa la distancia (en metros) entre las cargas. Finalmente, F representa la fuerza de la carga, medida en Newtons.

i. Resuelve la fórmula (3) para r.

ii. Dada una fuerza (F = 2.0 times 10 ^ {12} mathrm {N} ), dos cargas iguales (q_ {1} = q_ {2} = 1 mathrm {C} ), encuentre el aproximado distancia entre las dos partículas cargadas.

Respuesta

Multiplica en cruz, luego divide por el coeficiente de r.

[ begin {alineado} F & = k_ {C} frac {q_ {1} q_ {2}} {r ^ {2}} \ F r ^ {2} & = k_ {C} q_ {1} q_ {2} \ r ^ {2} & = frac {k_ {C} q_ {1} q_ {2}} {F} end {alineado} ]

Finalmente, para encontrar r, saca la raíz cuadrada.

[r = sqrt { frac {k_ {C} q_ {1} q_ {2}} {F}} ]

Para encontrar la distancia entre las partículas cargadas, sustituya (k_ {C} = 8.988 times 10 ^ {9} mathrm {Nm} ^ {2} / mathrm {C} ^ {2} ),
(q_ {1} = q_ {2} = 1 mathrm {C}, ) y (F = 2.0 times 10 ^ {12} mathrm {N} ).

[r = sqrt { frac { left (8.988 times 10 ^ {9} right) (1) (1)} {2.0 times 10 ^ {12}}} ]

Una calculadora produce una aproximación, (r aproximadamente 0.067 ) metros.

$Screen Shot 2019-07-26 at 4.24.57 PM.png$

Realice cada una de las siguientes tareas en los Ejercicios ( PageIndex {96} ) – ( PageIndex {99} ).

i. Escriba en palabras el significado de los símbolos que están escritos en notación de creador de set.

ii. Escribe algunos de los elementos de este conjunto.

iii. Dibuje una línea real y trace algunos de los puntos que están en este conjunto.

Ejercicio ( PageIndex {96} )

(A = {x in mathbb {N}: x> 10 } )

Respuesta

i. A es el conjunto de todas las x en los números naturales, de modo que x es mayor que 10.

ii. (A = {11,12,13,14, ldots } )

iii.

$Screen Shot 2019-08-05 at 10.42.27 AM.png$

Ejercicio ( PageIndex {97} )

(B = {x in mathbb {N}: x geq 10 } )

Ejercicio ( PageIndex {98} )

(C = {x in mathbb {Z}: x leq 2 } )

Respuesta

i. C es el conjunto de todas las x en los enteros, de modo que x es menor o igual que 2.

ii. (C = { ldots, -4, -3, -2, -1,0,1,2 } )

iii.

$Screen Shot 2019-08-05 at 10.43.52 AM.png$

Ejercicio ( PageIndex {99} )

(D = {x in mathbb {Z}: x> -3 } )

En los Ejercicios ( PageIndex {100} ) – ( PageIndex {103} ), use los conjuntos A, B, C y D que se definieron en los Ejercicios ( PageIndex {96} ) – ( PageIndex {99} ). Describa los siguientes conjuntos utilizando la notación de conjuntos y dibuje el Diagrama de Venn correspondiente.

Ejercicio ( PageIndex {100} )

(A cap B )

Respuesta

(A cap B = {x in mathbb {N}: x> 10 } = {11,12,13, ldots } )

$Screen Shot 2019-08-05 at 10.44.45 AM.png$

Ejercicio ( PageIndex {101} )

(A copa B )

Ejercicio ( PageIndex {102} )

(A copa C )

Respuesta

(A cup C={x in mathbb{Z} : x leq 2 text { or } x>10}={ldots,-3,-2-1,0,1,2,11,12,13 dots})

$Screen Shot 2019-08-05 at 10.45.52 AM.png$

Exercise (PageIndex{103})

(C cap D)

In Exercises (PageIndex{104})-(PageIndex{111}), use both interval and set notation to describe the interval shown on the graph.

Exercise (PageIndex{104})

$Screen Shot 2019-07-29 at 10.11.48 PM.png$

Answer: The filled circle at the endpoint 3 indicates this point is included in the set. Thus, the set in interval notation is ([3, infty)), and in set notation ({x : x geq 3}).

Exercise (PageIndex{105})

$Screen Shot 2019-07-29 at 10.12.57 PM.png$

Exercise (PageIndex{106})

$Screen Shot 2019-07-29 at 10.13.31 PM.png$

Answer: The empty circle at the endpoint −7 indicates this point is not included in the set. Thus, the set in interval notation is ((-infty,-7)), and in set notation is ({x : x<-7}).

Exercise (PageIndex{107})

$Screen Shot 2019-07-29 at 10.15.43 PM.png$

Exercise (PageIndex{108})

$Screen Shot 2019-07-29 at 10.16.40 PM.png$

Answer: The empty circle at the endpoint 0 indicates this point is not included in the set. Thus, the set in interval notation is ((0, infty)), and in set notation is ({x : x>0}).

Exercise (PageIndex{109})

$Screen Shot 2019-07-29 at 10.18.30 PM.png$

Exercise (PageIndex{110})

$Screen Shot 2019-07-29 at 10.19.29 PM.png$

Answer: The empty circle at the endpoint −8 indicates this point is not included in the set. Thus, the set in interval notation is ((-8, infty)), and in set notation is ({x : x>-8}).

Exercise (PageIndex{111})

$Screen Shot 2019-07-29 at 10.20.24 PM.png$

In Exercises (PageIndex{112})-(PageIndex{119}), sketch the graph of the given interval.

Exercise (PageIndex{112})

([2,5))

Answer: $Screen Shot 2019-08-05 at 10.49.22 AM.png$

Exercise (PageIndex{113})

((-3,1])

Exercise (PageIndex{114})

([1, infty))

Answer: $Screen Shot 2019-08-05 at 10.50.00 AM.png$

Exercise (PageIndex{115})

((-infty, 2))

Exercise (PageIndex{116})

({x :-4

Answer: $Screen Shot 2019-08-05 at 10.50.50 AM.png$

Exercise (PageIndex{117})

({x : 1 leq x leq 5})

Exercise (PageIndex{118})

({x : x<-2})

Answer: $Screen Shot 2019-08-05 at 10.51.30 AM.png$

Exercise (PageIndex{119})

({x : x geq-1})

In Exercises (PageIndex{120})-(PageIndex{127}), use both interval and set notation to describe the intersection of the two intervals shown on the graph. Also, sketch the graph of the intersection on the real number line.

Exercise (PageIndex{120})

$Screen Shot 2019-07-29 at 10.25.01 PM.png$

Answer

The intersection is the set of points that are in both intervals (shaded on both graphs). Graph of the intersection:

$Screen Shot 2019-08-05 at 10.52.32 AM.png$

([1, infty)={x : x geq 1})

Exercise (PageIndex{121})

$Screen Shot 2019-07-29 at 10.26.55 PM.png$

Exercise (PageIndex{122})

$Screen Shot 2019-07-29 at 10.27.31 PM.png$

Answer

There are no points that are in both intervals (shaded in both), so there is no intersection. Graph of the intersection:

$Screen Shot 2019-08-05 at 10.53.41 AM.png$

no intersection

Exercise (PageIndex{123})

$Screen Shot 2019-07-29 at 10.28.18 PM.png$

Exercise (PageIndex{124})

$Screen Shot 2019-07-29 at 10.29.22 PM.png$

Answer

The intersection is the set of points that are in both intervals (shaded in both). Graph of the intersection:

$Screen Shot 2019-08-05 at 10.54.24 AM.png$

([-6,2]={x :-6 leq x leq 2})

Exercise (PageIndex{125})

$Screen Shot 2019-07-29 at 10.30.25 PM.png$

Exercise (PageIndex{126})

$Screen Shot 2019-07-29 at 10.31.23 PM.png$

Answer

The intersection is the set of points that are in both intervals (shaded in both). Graph of the intersection:

$Screen Shot 2019-08-05 at 10.55.19 AM.png$

([9, infty)={x : x geq 9})

Exercise (PageIndex{127})

$Screen Shot 2019-07-29 at 10.33.57 PM.png$

In Exercises (PageIndex{128})-(PageIndex{135}), use both interval and set notation to describe the union of the two intervals shown on the graph. Also, sketch the graph of the union on the real number line.

Exercise (PageIndex{128})

$Screen Shot 2019-07-29 at 10.37.45 PM.png$

Answer

The union is the set of all points that are in one interval or the other (shaded in either graph). Graph of the union:

$Screen Shot 2019-08-05 at 10.58.47 AM.png$

((-infty,-8]={x : x leq-8})

Exercise (PageIndex{129})

$Screen Shot 2019-07-29 at 10.39.08 PM.png$

Exercise (PageIndex{130})

$Screen Shot 2019-07-29 at 10.39.38 PM.png$

Answer

The union is the set of all points that are in one interval or the other (shaded in either graph). Graph of the union:

$Screen Shot 2019-08-05 at 11.01.44 AM.png$

((-infty, 9] cup(15, infty))
(={x : x leq 9 text { or } x>15})

Exercise (PageIndex{131})

$Screen Shot 2019-07-29 at 10.40.55 PM.png$

Exercise (PageIndex{132})

$Screen Shot 2019-07-29 at 10.42.41 PM.png$

Answer

The union is the set of all points that are in one interval or the other (shaded in either). Graph of the union:

$Screen Shot 2019-08-05 at 11.03.02 AM.png$

((-infty, 3)={x : x<3})

Exercise (PageIndex{133})

$Screen Shot 2019-07-29 at 10.44.52 PM.png$

Exercise (PageIndex{134})

$Screen Shot 2019-07-29 at 10.45.57 PM.png$

Answer

The union is the set of all points that are in one interval or the other (shaded in either). Graph of the union:

$Screen Shot 2019-08-05 at 11.04.38 AM.png$

([9, infty)={x : x geq 9})

Exercise (PageIndex{135})

$Screen Shot 2019-07-29 at 10.46.54 PM.png$

In Exercises (PageIndex{136})-56, use interval notation to describe the given set. Also, sketch the graph of the set on the real number line.

Exercise (PageIndex{136})

({x : x geq-6 text { and } x>-5})

Answer

This set is the same as ({x : x>-5}), which is ((-5, infty)) in interval notation. Graph of the set:

$Screen Shot 2019-08-05 at 11.06.12 AM.png$

Exercise (PageIndex{137})

({x : x leq 6 text { and } x geq 4})

Exercise (PageIndex{138})

({x : x geq-1 text { or } x<3})

Answer

Every real number is in one or the other of the two intervals. Therefore, the set is the set of all real numbers ((-infty, infty)). Graph of the set:

$Screen Shot 2019-08-05 at 11.07.04 AM.png$

Exercise (PageIndex{139})

({x : x>-7 text { and } x>-4})

Exercise (PageIndex{140})

({x : x geq -1 text { or } x>6})

Answer

This set is the same as ({x : x geq-1}), which is ([-1, infty)) in interval notation. Graph of the set:

$Screen Shot 2019-08-05 at 11.10.10 AM.png$

Exercise (PageIndex{141})

({x : x geq 7 text { or } x<-2})

Exercise (PageIndex{142})

({x : x geq 6 text { or } x>-3})

Answer

This set is the same as ({x : x>-3}), which is ((-3, infty)) in interval notation. Graph of the set:

$Screen Shot 2019-08-05 at 11.12.01 AM.png$

Exercise (PageIndex{143})

({x : x leq 1 text { or } x>0})

Exercise (PageIndex{144})

({x : x<2 text { and } x<-7})

Answer

This set is the same as ({x : x<-7}), which is ((-infty,-7)) in interval notation. Graph of the set:

$Screen Shot 2019-08-05 at 11.13.07 AM.png$

Exercise (PageIndex{145})

({x : x leq-3 text { and } x<-5})

Exercise (PageIndex{146})

({x : x leq-3 text { or } x geq 4})

Answer

This set is the union of two intervals, ((-infty,-3] cup[4, infty)). Graph of the set:

$Screen Shot 2019-08-05 at 11.14.04 AM.png$

Exercise (PageIndex{147})

({x : x<11 text { or } x leq 8})

Exercise (PageIndex{148})

({x : x geq 5 text { and } x leq 1})

Answer

There are no numbers that satisfy both inequalities. Thus, there is no intersection. Graph of the set:

$Screen Shot 2019-08-05 at 11.14.56 AM.png$

Exercise (PageIndex{149})

({x : x<5 text { or } x<10})

Exercise (PageIndex{150})

({x : x leq 5 text { and } x geq-1})

Answer

This set is the same as ({x :-1 leq x leq 5}), which is [−1, 5] in interval notation. Graph of the set

$Screen Shot 2019-08-05 at 11.17.54 AM.png$

Exercise (PageIndex{151})

({x : x>-3 text { and } x<-6})

In Exercises (PageIndex{152})-(PageIndex{163}), solve the inequality. Express your answer in both interval and set notations, and shade the solution on a number line.

Exercise (PageIndex{152})

(-8 x-3 leq-16 x-1)

Answer

[begin{aligned} & -8 x-3 leq-16 x-1 \ Longrightarrow quad & − 8x + 16x leq −1 + 3 \ Longrightarrow quad& 8x leq 2 \ Longrightarrow quad & x leq frac{1}{4}end{aligned}]

Thus, the solution interval is ((−infty, frac{1}{4}]) = ({x|x leq frac{1}{4}}).

$Screen Shot 2019-08-07 at 10.21.02 PM.png$

Exercise (PageIndex{153})

(6 x-6>3 x+3)

Exercise (PageIndex{154})

(-12 x+5 leq-3 x-4)

Answer

[begin{aligned} & -12 x+5 leq-3 x-4 \ Longrightarrow quad & -12x + 3x leq −4 − 5 \ Longrightarrow quad& -9x leq -9 \ Longrightarrow quad & x geq 1end{aligned}]

Thus, the solution interval is ([1,infty) = {x|x geq 1}).

$Screen Shot 2019-08-08 at 10.56.57 PM.png$

Exercise (PageIndex{155})

(7 x+3 leq-2 x-8)

Exercise (PageIndex{156})

(-11 x-9<-3 x+1)

Answer

[begin{aligned} & − 11x − 9 < −3x + 1 \ Longrightarrow quad & − 11x + 3x < 1 + 9 \ Longrightarrow quad& − 8x < 10 \ Longrightarrow quad & x > -frac{5}{4}end{aligned}]

Thus, the solution interval is ((−frac{5}{4} ,infty) = {x|x >−frac{5}{4} }).

$Screen Shot 2019-08-08 at 11.00.01 PM.png$

Exercise (PageIndex{157})

(4 x-8 geq-4 x-5)

Exercise (PageIndex{158})

(4 x-5>5 x-7)

Answer

[begin{aligned} & 4x − 5 > 5x − 7\ Longrightarrow quad & 4x − 5x > −7 + 5 \ Longrightarrow quad& − x > −2 \ Longrightarrow quad &x < 2end{aligned}]
Thus, the solution interval is ((−infty, 2) = {x|x < 2}).

$Screen Shot 2019-08-08 at 11.02.23 PM.png$

Exercise (PageIndex{159})

(-14 x+4>-6 x+8)

Exercise (PageIndex{160})

(2 x-1>7 x+2)

Answer

[begin{aligned} & 2x − 1 > 7x + 2\ Longrightarrow quad & 2x − 7x > 2 + 1 \ Longrightarrow quad& − 5x > 3 \ Longrightarrow quad &x < −frac{3}{5}end{aligned}]
Thus, the solution interval is ((−infty, −frac{3}{5}) = {x|x < −frac{3}{5}}).

$Screen Shot 2019-08-08 at 11.04.53 PM.png$

Exercise (PageIndex{161})

(-3 x-2>-4 x-9)

Exercise (PageIndex{162})

(-3 x+3<-11 x-3)

Answer

[begin{aligned} & − 3x + 3 < −11x − 3\ Longrightarrow quad & − 3x + 11x < −3 − 3 \ Longrightarrow quad& 8x < −6 \ Longrightarrow quad &x < -frac{3}{4}end{aligned}]
Thus, the solution interval is ((−infty, −frac{3}{4}) = {x|x < −frac{3}{4}}).

$Screen Shot 2019-08-08 at 11.07.23 PM.png$

Exercise (PageIndex{163})

(6 x+3<8 x+8)

In Exercises 13-50, solve the compound inequality. Express your answer in both interval and set notations, and shade the solution on a number line.

Exercise (PageIndex{164})

(2 x-1<4) or (7 x+1 geq-4)

Answer

[begin{aligned} & 2x − 1 < 4 text{ or } 7x + 1 geq −4\ Longrightarrow quad & 2x < 5quad text{or}quad 7x geq −5 \ Longrightarrow quad&x

$Screen Shot 2019-08-08 at 11.11.56 PM.png$

For the union, shade anything shaded in either graph. The solution is the set of all real numbers ((−infty,infty)).

$Screen Shot 2019-08-08 at 11.13.59 PM.png$

Exercise (PageIndex{165})

(-8 x+9<-3) and (-7 x+1>3)

Exercise (PageIndex{166})

(-6 x-4<-4) and (-3 x+7 geq-5)

Answer

[begin{aligned} & − 6x − 4 < −4 text{ and } − 3x + 7 geq −5\ Longrightarrow quad & -6x < 0quad text{and}quad -3x geq −12 \ Longrightarrow quad&x>0quadtext{and}quad xleq4 \ Longrightarrow quad & 0< x leq 4 end{aligned}]

$Screen Shot 2019-08-08 at 11.21.51 PM.png$

The intersection is all points shaded in both graphs, so the solution is ((0, 4] = {x|0 < x leq 4}).

$Screen Shot 2019-08-08 at 11.23.30 PM.png$

Exercise (PageIndex{167})

(-3 x+3 leq 8) and (-3 x-6>-6)

Exercise (PageIndex{168})

(8 x+5 leq-1) and (4 x-2>-1)

Answer: Add texts here. Do not delete this text first.

Exercise (PageIndex{169})

(-x-1<7) and (-6 x-9 geq 8)

Exercise (PageIndex{170})

(-3 x+8 leq-5) or (-2 x-4 geq-3)

Answer: Add texts here. Do not delete this text first.

Exercise (PageIndex{171})

(-6 x-7<-3) and (-8 x geq 3)

Exercise (PageIndex{172})

(9 x-9 leq 9) and (5 x>-1)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-7 x+3<-3) or (-8 x geq 2)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(3 x-5<4) and (-x+9>3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-8 x-6<5) or (4 x-1 geq 3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(9 x+3 leq-5) or (-2 x-4 geq 9)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-7 x+6<-4) or (-7 x-5>7)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(4 x-2 leq 2) or (3 x-9 geq 3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-5 x+5<-4) or (-5 x-5 geq-5)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(5 x+1<-6) and (3 x+9>-4)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(7 x+2<-5) or (6 x-9 geq-7)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-7 x-7<-2) and (3 x geq 3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(4 x+1<0) or (8 x+6>9)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(7 x+8<-3) and (8 x+3 geq-9)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(3 x<2) and (-7 x-8 geq 3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-5 x+2 leq-2) and (-6 x+2 geq 3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(4 x-1 leq 8) or (3 x-9>0)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(2 x-5 leq 1) and (4 x+7>7)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(3 x+1<0) or (5 x+5>-8)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-8 x+7 leq 9) or (-5 x+6>-2)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(x-6 leq-5) and (6 x-2>-3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-4 x-8<4) or (-4 x+2>3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(9 x-5<2) or (-8 x-5 geq-6)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-9 x-5 leq-3) or (x+1>3)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-5 x-3 leq 6) and (2 x-1 geq 6)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-1 leq-7 x-3 leq 2)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(0<5 x-5<9)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(5<9 x-3 leq 6)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-6<7 x+3 leq 2)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-2<-7 x+6<6)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-9<-2 x+5 leq 1)

Answer: Add texts here. Do not delete this text first.

In Exercises 51-62, solve the given inequality for x. Graph the solution set on a number line, then use interval and setbuilder notation to describe the solution set.

Ejercicio ( PageIndex {1} )

(-frac{1}{3}

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-frac{1}{5}

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-frac{1}{2}

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-frac{2}{3} leq frac{1}{2}-frac{x}{5} leq frac{2}{3})

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-1

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-2

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-2

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-3

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(x<4-x<5)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-x<2 x+3 leq 7)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(-x

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

(−2x < 3 − x leq 8)

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )

Aeron has arranged for a demonstration of “How to make a Comet” by Professor O’Commel. The wise professor has asked Aeron to make sure the auditorium stays between 15 and 20 degrees Celsius (C). Aeron knows the thermostat is in Fahrenheit (F) and he also knows that the conversion formula between the two temperature scales is C = (5/9)(F − 32).

a) Setting up the compound inequality for the requested temperature range in Celsius, we get (15 leq C leq 20). Using the conversion formula above, set up the corresponding compound inequality in Fahrenheit.

b) Solve the compound inequality in part (a) for F. Write your answer in set notation.

c) What are the possible temperatures (integers only) that Aeron can set the thermostat to in Fahrenheit?

Answer: Add texts here. Do not delete this text first.

Ejercicio ( PageIndex {1} )