Deck 4: Inequalities and Problem Solving

Question 1

Solve.
ABC phone company charges $21 per month plus 8¢ per minute of phone calls. XYZ phone company charges $15 per month plus 10¢ per minute of phone calls. How many minutes of phone calls in a month make XYZ phone company the better deal?

A) More than 30 minutes
B) Less than 300 minutes
C) Less than 30 minutes
D) More than 300 minutes

Answer 1

B

Question 2

Solve the inequality. Other than Ø, graph the solution set on a number line.
$$\frac { x } { 3 } \geq 4 + \frac { x } { 15 }$$

A) $( - \infty , 15 ]$

B) $[ 15 , \infty )$

C) $[ - 15 , \infty )$

D) $( 15 , \infty )$
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Answer 2

B

Question 3

Solve.
When making a long distance call from a certain pay phone, the first three minutes of a call cost $1.15. After that, each additional minute or portion of a minute of that call costs $0.20. Use an inequality to find the number of minutes one can call long distance for $2.15.

A) 5 minutes or fewer
B) 11 minutes or fewer
C) 2 minutes or fewer
D) 8 minutes or fewer

Answer 3

D

Question 4

Solve.
Claire has received scores of 85, 88, 87, and 95 on her algebra tests. What score must she receive on the fifth test to have an overall test score average of at least 90?

A) 93 or greater
B) 95 or greater
C) 94 or greater
D) 96 or greater

Question 5

Solve.
It takes 22 minutes to set up a candy making machine. Once the machine is set up, it produces 10 candies per minute. Use an inequality to find the number of candies that can be produced in 2 hours if the machine has not yet been set up.

A) 980 candies or fewer
B) 20 candies or fewer
C) 440 candies or fewer
D) 2420 candies or fewer

Question 6

Solve the inequality. Other than Ø, graph the solution set on a number line.
$$4 x + 1 < 29$$

A) $( * , 7 )$

B) $( 7 , \infty )$

C) $( * , 7 ]$

D) $[ 7 , \infty )$

Question 7

Solve the inequality. Other than Ø, graph the solution set on a number line.
$4 x - 3 \geq 3 x - 9$

$A ) [ - 6 , \infty )$

B) $( - \infty , - 6 )$

C) $( - 6 , \infty )$

D) $( - \infty , - 6 ]$

Question 8

Solve the inequality. Other than Ø, graph the solution set on a number line.
$- 2 ( 2 x - 8 ) < - 6 x + 2$

A) $( - 7 , \infty )$

B) $[ - 7 , \infty )$

C) $( \infty , - 7 ]$

D) $( \infty , - 7 )$

Question 9

Solve the inequality. Other than Ø, graph the solution set on a number line.
$$- 4 x \geq 24$$

A) $( * , - 6 ]$

B) $[ 6 , \infty )$

C) $( x , 6 ]$

D) $[ - 6 , \infty )$

Question 10

Solve.
Using data from 2010-2012, the annual number of cars sold at a certain dealership can be modeled by the formula y = 4x + 3, where y is the number of cars, in thousands, sold x years after 2010. According to this formula, in which years will the number of cars sold exceed 31 thousand?

A) Years after 2017
B) Years after 2019
C) Years after 2021
D) Years after 2015

Question 11

Solve.
A certain store has a fax machine available for use by its customers. The store charges $2.00 to send the first page and $0.50 for each subsequent page. Use an inequality to find the number of pages that can be faxed for $6.00.

A) 3 pages or fewer
B) 9 pages or fewer
C) 12 pages or fewer
D) 48 pages or fewer

Question 12

Solve the inequality. Other than Ø, graph the solution set on a number line.
$$- 6 x + 8 - 4 x < 8 - 12 x + 6$$

A) $( 3 , \infty )$

B) $( \infty , 3 )$

C) $( \infty , 3 ]$

D) $[ 3 , \infty )$

Question 13

Solve the inequality. Other than Ø, graph the solution set on a number line.
$$\frac { x - 3 } { 9 } \geq \frac { x - 5 } { 12 } + \frac { 1 } { 36 }$$

A) $( - \infty , - 2 ]$

B) $( - \infty , - 2 )$

C) $[ - 2 , \infty )$

D) $( - 2 , \infty )$

Question 14

Solve the inequality. Other than Ø, graph the solution set on a number line.
$$8 x - 10 \leq 2 x - 15$$

A) $[ - 5,6 ]$

B) $\left( - \infty , - \frac { 5 } { 6 } \right)$

C) $( - 5,6 )$

D) $\left[ - \infty , - \frac { 5 } { 6 } \right]$

Question 15

Solve the linear inequality. Other than Ø, graph the solution set on a number line.
$$5 ( 4 x + 5 ) - 4 x < 4 ( 6 + 4 x ) - 6$$

A) $( \infty , 5 )$

B) $\varnothing$
C) $( \infty , \infty )$

D) $( 5 , \infty )$

Question 16

Solve.
Greg is opening a car wash. He estimates his cost equation as C = 8000 + 0.08x and his revenue equation as R = 1.85x, where x is the number of cars washed in a six-month period. Find the number of cars that must be washed in a six-month period for Greg to make a profit.

A) At least 45,198 cars
B) At least 4520 cars
C) At least 3520 cars
D) At least 452 cars

Question 17

Solve the linear inequality. Other than Ø, graph the solution set on a number line.
$$4 ( x + 7 ) \geq 3 ( x - 6 ) + x$$

A) $( x , \infty )$

B) $\varnothing$

C) $[ 3 , \infty )$

D) $( \infty , 3 ]$

Question 18

Solve the inequality. Other than Ø, graph the solution set on a number line.
$14 x - 18 > 2 ( 6 x - 4 )$

A) $[ 5 , \infty )$




$\text { C) }(*, 5]$

$\text { D) }(5, \infty)$

Question 19

Solve the linear inequality. Other than Ø, graph the solution set on a number line.
$$- 5 x \leq - 5 ( x - 6 )$$

A) $\varnothing$
B) $( \infty , - 6 ]$

C) $( \infty , \infty )$

D) $[ - 6 , \infty )$

Question 20

Solve the inequality. Other than Ø, graph the solution set on a number line.
$$\frac { x } { 6 } - \frac { 1 } { 4 } \leq \frac { x } { 3 } + 2$$

A) $\left[ - \frac { 27 } { 2 } , \infty \right)$

B) $\left( * , - \frac { 27 } { 2 } \right)$

C) $\left[ \infty , - \frac { 27 } { 2 } \right]$

D) $\left( - \frac { 27 } { 2 } , \infty \right)$

Question 21

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$$17 \leq \frac { 9 x } { 7 } + 8 < 26$$

A) $( 7,14 ]$

B) $( 7,8 ]$

C) $[ 7,14 )$

D) $[ 7,8 )$

Question 22

Solve.
A standard train ticket in a certain city costs $1.50 per ride. People who use the train also have the option of purchasing a frequent-rider pass for $15.00 each month. With the pass, a ticket costs only $0.75 per ride. How many train rides in a month make the frequent-rider pass a better deal than standard train tickets?

A) 22 or more rides
B) 19 or more rides
C) 21 or more rides
D) 20 or more rides

Question 23

Solve.
Every Sunday, Jarod buys a loaf of fresh bread for his family from the corner bakery for $2.00. The local department store has a sale on breadmakers for $83. If the bread-making supplies cost $0.93 per week, for how many weeks would Jarod have to bake a loaf of bread at home before the breadmaker starts saving him money?

A) At least 80 weeks
B) At least 77 weeks
C) At least 78 weeks
D) At least 79 weeks

Question 24

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$20 < 5 x \leq 25$

A) $( - \infty , 4 ] \cup ( 5 , \infty )$

B) $[ 4,5 )$

C) $( 4,5 ]$

D) $( - \infty , 4 ) \cup [ 5 , \infty )$

Question 25

Find the intersection of the sets.
$$\{ - 5 , - 1,2,6 \} \cap \{ - 4,1,5,8 \}$$

A) $\{ 1 \}$
B) $\{ - 5 , - 4 , - 1,1,2,5,6,8 \}$
C) $\varnothing$
D) $\{ - 1,1,2 \}$

Question 26

Find the intersection of the sets.
$\{ a , e , o , u \} \cap \varnothing$

A) $\{ a \}$
B) $\varnothing$
C) $\{ \mathrm { u } \}$
D) $\{ a , e , o , u \}$

Question 27

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$4 x < 12$ and $x + 4 > 5$

A) $[ 1,3 ]$

B) $( 1,3 )$

C) $( - \infty , 1 ) \cup ( 3 , \infty )$

D)
$\varnothing$

Question 28

Solve. Use interval notation to express the range.
The formula for converting Fahrenheit temperature, $F$ , to Celsius temperature, $C$ , is
$$C = \frac { 5 } { 9 } ( F - 32 ) \text {. }$$
If Celsius temperature ranges from $- 10 ^ { \circ }$ to $45 ^ { \circ }$ , inclusive, what is the range for the Fahrenheit temperature?

A) $[ 14,113 ]$
B) $( - 19 , - 13 )$
C) $( 14,113 )$
D) $[ - 19 , - 13 ]$

Question 29

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$- 7 x > - 7$ and $x + 7 > 5$

$A ) ( 1 , \infty )$

B) $( - 2,1 )$

$C ) ( - \infty , - 2 ) \cup ( 1 , \infty )$

D)
$\phi$

Question 30

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$-4 x<-12 \text { and } x+4>5$

A) $( 1,3 )$

B) $\varnothing$

C) $( 3 , \infty )$

D) $( - \infty , 1 ) \cup ( 3 , \infty )$

Question 31

Solve. Use interval notation to express the range.
The formula for converting Celsius temperature, $C$ , to Fahrenheit temperature, $F$ , is
$$\mathrm { F } = \frac { 9 } { 5 } \mathrm { C } + 32 \text {. }$$
If Fahrenheit temperature ranges from $41 ^ { \circ }$ to $176 ^ { \circ }$ , inclusive, what is the range for the Celsius temperature?

A) $( 5,80 )$
B) $[ 106,349 ]$
C) $[ 5,80 ]$
D) $( 106,349 )$

Question 32

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$x+6<3 \text { and }-6 x<-6$

A)
$\phi$
B) $( - \infty , - 3 )$

C) $( - 3,1 )$

D) $( - \infty , - 3 ) \cup ( 1 , \infty )$

Question 33

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$-31 \leq-4 x-3<-15$

A) $\varnothing$

B) $[ 3,7 )$

C) $( 3,7 ]$

D) $( - \infty , 3 ] \cup ( 7 , \infty )$

Question 34

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$x \leq 1$ anc $x \geq - 2$

A) $\phi$
B) $( - \infty , - 2 ] \cup [ 1 , \infty )$

C) $[ - 2,1 ]$

D) $( - 2,1 )$
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Question 35

Find the intersection of the sets.
$\{ - 4,0,2,5 \} \cap \{ 2,5,8 \}$

A) $\{ 2,5,8 \}$
B) $\{ - 4,0,2,5,8 \}$
C) $\{ - 4,0,2,5 \}$
D) $\{ 2,5 \}$

Question 36

Solve. Use interval notation to express the range.
On the first four exams, your grades are 79, 82, 75, and 80. There is still a final exam, and it counts as two grades. You are hoping to earn a C in the course. This will occur if the average of your six exam grades is greater than or equal to 70 and less than 80. What range of grades on the final exam will result in earning a C?

A) [52, 82)
B) [52, 82]
C) [34, 84]
D) [34, 84)

Question 37

Solve. Use interval notation to express the range.
On the first four exams, your grades are 79, 89, 68, and 80. You are hoping to earn a C in the course. This will occur if the average of your five exam grades is greater than or equal to 70 and less than 80. What range of grades on the fifth exam will result in earning a C?

A) (24, 74]
B) [34, 84)
C) (34, 84]
D) [24, 74)

Question 38

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$8\leq 2 x + 4 \leq 18$

$\text { A) }(-\infty, 2) \cup(7, \infty)$

$\text { B) }[2,7]$

C) $( 2,7 )$

D) $( - \infty , 2 ] \cup [ 7 , \infty )$

Question 39

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$x \leq 3$ and $x \leq 1$

A) $[ 1,3 ]$


B) $( - \infty , 1 ] \cup [ 3 , \infty )$

C) $( - \infty , 3 ]$

D) $( - \infty , 1 ]$

Question 40

Solve. Use interval notation to express the range.
Parts for an automobile repair cost $609. The mechanic charges $29 per hour. If you receive an estimate for at least $783 and at most $870 for fixing the car, what is the time interval that the mechanic will be working on the job?

A) [6, 9]
B) [1, 9]
C) [1, 6]
D) [27, 30]

Question 41

Find the solution set for the equation.
$$| x - 5 | = 4$$

A) $\varnothing$
B) $\{ 1,9 \}$
C) $\{ - 9 \}$
D) $\{ - 1,9 \}$

Question 42

Find the solution set for the equation.
$\left| \frac { 2 x + 5 } { 3 } \right| = 3$

A) $\{ - 2 \}$
B) $\{ 7 \}$
C) $\{ 2 , - 7 \rangle$
D) $\varnothing$

Question 43

Find the solution set for the equation.
$$| x | = 6$$

A) $\{ 36 \}$
B) $\{ - 6 \}$
C) $\{ - 6,6 \}$
D) $\{ 6 \}$

Question 44

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$\mathrm { X } > 4 \mathrm { Or } x < 4$

A) $( - \infty , 4 )$

B) $\left( \frac { 4 } { 4 } ( x ) \right)$

C)
$\phi$

D) $( - \infty , 4 ) \cup ( 4 , \infty )$

Question 45

Solve. Use interval notation to express the range.
The formula C = 0.5x + 18 represents the estimated future cost of yearly attendance at State University, where C is the cost in thousands of dollars x years after 2010. Use a compound inequality to determine in which years attendance costs will range from 22 to 24 thousand dollars.

A) [2017, 2021]
B) [2018, 2022]
C) [2019, 2023]
D) [2019, 2021]

Question 46

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$- 4 x + 1 \geq 9$ or $6 x + 3 \geq - 21$

A) $( - \infty , \infty )$

B) $[ - 4 , \infty )$

C) $[ - 4 , - 2 ]$

D) $[ - 2 , \infty )$

Question 47

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$x < 4$ or $x < 8$

A) $( - \infty , 4 )$

B) $( 4,8 )$
C)
$( - \infty , 4 ) \cup ( 8 , \infty )$

D) $( - \infty , 8 )$

Question 48

Find the union of the sets.
{-5, -2, 1, 4} ∪ {1, 4, 7}

A) {1, 4}
B) {1, 4, 7}
C) {-5, -2, 1, 4}
D) {-5, -2, 1, 4, 7}

Question 49

Find the solution set for the equation.
$$| 4 x + 9 | = | x - 4 |$$

A) $\left\{ \frac { 13 } { 3 } , 1 \right\}$
B) $\left\{ - \frac { 13 } { 3 } , \frac { 22 } { 5 } \right\}$
C) $\varnothing$
D) $\left\{ - \frac { 13 } { 3 } , - 1 \right\}$

Question 50

Solve and graph the solution set on a number line.
$|x|<8$

A) $( - \infty , - 8 ) \cup ( 8 , \infty )$

B) $[ - 8,8 ]$

C) $( - 8,8 )$

D) $( - \infty , - 8 ] \cup [ 8 , \infty )$

Question 51

Find the solution set for the equation.
$$| 7 x + 6 | + 9 = 13$$

A) $\left\{ - \frac { 1 } { 3 } , - \frac { 5 } { 3 } \right\}$
B) $\left\{ \frac { 2 } { 7 } , \frac { 10 } { 7 } \right\}$
C) $\varnothing$
D) $\left\{ - \frac { 2 } { 7 } , - \frac { 10 } { 7 } \right\}$

Question 52

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$x \leq 4 { } ^ { A } x \geq 8$

$A ) [ 4,8 ]$

B)
$\phi$

C $( - \infty , 4 ] \cup [ 8 , \infty )$

D $( 4,8 )$

Question 53

Find the solution set for the equation.
$$| 7 x - 7 | + 4 = 1$$

A) $\left\{ \frac { 4 } { 7 } , - \frac { 10 } { 7 } \right\}$
B) $\left\{ \frac { 10 } { 7 } , - \frac { 4 } { 7 } \right\}$
C) $\left\{ \frac { 4 } { 7 } \right\}$
D) $\varnothing$

Question 54

Find the solution set for the equation.
$$| 3 x + 2 | = | 3 x - 2 |$$

A) $\{ 0,3 \}$
B) $\{ 0,2 \}$
C) $\{ 0 \}$
D) $\varnothing$

Question 55

Find the union of the sets.
$\{ w , h , a , t , s \} \cup \varnothing$

A) $\{ a , s \}$
B) $\{ w \}$
C) $\varnothing$
D) $\{ w , h , a , t , s \}$

Question 56

Find the solution set for the equation.
$$| x - 8 | = | 9 - x |$$

A) $\varnothing$
В) $\left\{ \frac { 17 } { 2 } \right\}$
C) $\left\{ \frac { 1 } { 2 } \right\}$
D) $\{ 17 \}$

Question 57

Solve the compound inequality and graph the solution set on a number line. Except for the empty set, express the solution set in interval notation.
$- 4 x \leq - 12$ or $4 x > 12 x - 8$

$\text { A) }(-\infty, 1] \cup(3, \infty)$

B) $( - \infty , 1 ) \cup [ 3 , \infty )$

C) $\varnothing$
D) $( 1,3 ]$

Question 58

Find the solution set for the equation.
$$3 | x - 3 | = 18$$

A) $\varnothing$
B) $\{ 3 \}$
C) $\{ 9 , - 3 \}$
D) $\{ 3 , - 9 \}$

Question 59

Find the union of the sets.
{-5, -1, 2, 6} ∪ {-3, 1, 4, 8}

A) {-1, 1, 2}
B) {-5, -3, -1, 1, 2, 4, 6, 8}
C) {1}
D) Ø

Question 60

Find the solution set for the equation.
$$| x - 9 | = 0$$

A) $\{ - 9 \}$
B) $\{ 9 \}$
C) $\varnothing$
D) $\{ - 9,9 \}$

Question 61

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
$| x - 5 | \geq 0$

A) $\{ 5 \}$

B) $( - 5,5 )$

C) $( 5 , \infty )$

D) $( - \infty , \infty )$

Question 62

Solve and graph the solution set on a number line.
$$2 + \left| 1 - \frac { x } { 2 } \right| \leq 5$$

A) $( - \infty , - 4 ] \cup [ 8 , \infty )$

B) $[ - 4,8 ]$

C) $( - \infty , - 8 ] \cup [ 4 , \infty )$

D) $[ - 8,4 ]$

Question 63

Solve and graph the solution set on a number line.
$| x - 9 | > 9$

A) $[ 0,18 ]$

B) $( 0,18 )$

C) $( - \infty , 0 ) \cup ( 18 , \infty )$

D)
$\varnothing$

Question 64

Solve and graph the solution set on a number line.

Question 65

Solve.
When a number is subtracted from -7, the absolute value of the difference is more than 3. Use interval notation to express the set of all numbers that satisfy this condition. A) $( \infty , - 4 ) \cup ( 10 , \infty )$
B) $( \infty , - 10 ) \cup ( - 4 , \infty )$
C) $( \infty , - 10 ] \cup [ - 4 , \infty )$
D) $( - 10 , - 4 )$

Question 66

Solve and graph the solution set on a number line.
$| x + 8 | \leq 0$

A) $( - \infty , - 8 )$

B) $\{ 8 \}$

C)
$\varnothing$

D) $\{ - 8 \}$

Question 67

Solve and graph the solution set on a number line.
$|x+3|-6 \leq-1$

A) $( - 8,2 )$

B) $[ - 8,2 ]$

$\text { C) } \varnothing$

D) [ - 8 , - 1 ]

Question 68

Solve.
The radius r of a plastic tube used in manufacturing a child's toy must not differ from the standard s by more than 5 millimeters. The manufacturing engineers express this as |r - s| ≤5. If the standard s is 33, solve the inequality for the radius r. Express the answer in set-builder notation. A) $\{ \mathrm { r } \mid 23 \leq \mathrm { r } \leq 28 \}$
B) $\{ \mathrm { r } \mid 28 \leq \mathrm { r } \leq 38 \}$
C) $\{ \mathrm { r } \mid \mathrm { r } \leq 28$ or $\mathrm { r } \geq 38 \}$
D) $\{ \mathrm { r } \mid \mathrm { r } \leq 23$ or $\mathrm { r } \geq 28 \}$

Question 69

Solve and graph the solution set on a number line.
$| 7 x + 9 | + 1 < 7$

A) $\left( - \infty , - \frac { 15 } { 7 } \right)$

B) $\left( - \frac { 3 } { 7 } , - \frac { 15 } { 7 } \right)$

$C ) \left( - \frac { 15 } { 7 } , - \frac { 3 } { 7 } \right)$

D)

Question 70

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
$| 5 x - 4 | - 6 > - 9$

A) $\varnothing$

B) $\left( \frac { 1 } { 5 } , \frac { 7 } { 5 } \right)$

C) $\left( \frac { 1 } { 5 } , \infty \right)$

D) $( - \infty , \infty )$

Question 71

Solve and graph the solution set on a number line.
$$| 3 ( x + 1 ) + 9 | \geq 15$$

A) $[ - 9,1 ]$

B) $( \infty , - 7 ] \cup [ 3 , \infty )$

C) $[ - 7,3 ]$

D) $( * , - 9 ] \cup [ 1 , \infty )$

Question 72

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
$$| 3 x - 3 | + 7 < - 1$$

A) $\varnothing$

B) $\left( - \infty , - \frac { 5 } { 3 } \right)$

C) $\left( - \infty , \frac { 11 } { 3 } \right)$

D) $\left( - \frac { 5 } { 3 } , \frac { 11 } { 3 } \right)$

Question 73

Solve and graph the solution set on a number line.
$$5 + \left| 1 - \frac { x } { 2 } \right| \geq 8$$

A) $[ - 8,4 ]$

B) $( - \infty , - 8 ] \cup [ 4 , \infty )$

C) $( - \infty , - 4 ] \cup [ 8 , \infty )$

D) $[ - 4,8 ]$

Question 74

Solve and graph the solution set on a number line.
$| x + 7 | < 6$

A) $Q$
B) $( - 13 , - 1 )$

C) $[ - 13 , - 1 ]$

D) $( - \infty , - 13 ) \cup ( - 1 , \infty )$

Question 75

Solve and graph the solution set on a number line. Express the solution set in both set-builder and interval notations.
$|x-3|<0$

A) $( - \infty , 3 )$

B) $( - 3 , \infty )$

C)
$\varnothing$
D) $( - 3,3 )$

Question 76

Solve and graph the solution set on a number line.
$| x - 9 | + 3 \geq 11$

A) $[ 1,17 ]$

B) $( - \infty , 1 ) \cup ( 17 , \infty )$

C) $( - \infty , 1 ] \cup [ 17 , \infty )$

$\text { D) } \phi$

Question 77

Solve and graph the solution set on a number line.
$$| x | > 6$$

A) $( - 6,6 )$

B) $( - \infty , - 6 ) \cup ( 6 , \infty )$

C) $( - \infty , - 6 ] \cup [ 6 , \infty )$

D) $[ - 6,6 ]$

Question 78

Solve.
The length ℓ of a metal rod used in manufacturing cars must not differ from the standard s by more than 0.3 inches. The manufacturing engineers express this as |ℓ- s| ≤0.3. If the standard s is 23.1, solve the inequality for the length ℓ. Express the answer in set-builder notation. A) $\{ \ell l \ell \leq 22.8$ or $\ell \geq 23.4 \}$
B) $\{ \ell l 22.8 \leq \ell \leq 23.4 \}$
C) $\{ \ell \mid 23.4 \leq \ell \leq 23.7 \}$
D) $\{$ ll $l \leq 23.4$ or $\ell \geq 23.7 \}$

Question 79

Solve and graph the solution set on a number line.
$| x + 9 | > 0$

A) $( - 9 , \infty )$

B) $( - \infty , - 9 ) \cup ( - 9 , \infty )$

$\text { (C) } \phi$
D) $( - 9,9 )$

Question 80

Solve and graph the solution set on a number line.
$$| 3 ( x + 1 ) + 6 | \leq 9$$

A) $( - 4,2 )$

B) $( - 6,0 )$

C) $[ - 6,0 ]$

D) $[ - 4,2 ]$