AnswersOC27 MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006PSolving Absolute Value Equations

Absolute Value Inequalities Answers

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What is the solution to –2|2.2x – 3.3| = –6.6?

A
x = –3
B
x = 3
C
x = –3 or x = 0
D
x = 0 or x = 3
2
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Which number line represents the solutions to |x + 4| = 2?

A
A number line from negative 7 to 7 in increments of 1. Two points, one at negative 6 and one at negative 2.
Option A
B
A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 4.
Option B
C
A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 6.
Option C
D
A number line from negative 7 to 7 in increments of 1. Two points, one at negative 4 and one at negative 2.
Option D
3

Which number line represents the solutions to |x – 5| = 1?

A
A number line from negative 7 to 7 in increments of 1. Two points, one at negative 6 and one at negative 4.
Option A
B
A number line from negative 7 to 7 in increments of 1. Two points, one at 4 and one at 6.
Option B
C
A number line from negative 7 to 7 in increments of 1. Two points, one at negative 5 and one at 1.
Option C
D
A number line from negative 7 to 7 in increments of 1. Two points, one at negative 1 and one at 5.
Option D
4

To win a contest, the number of beans in a jar has to be guessed within 20 of the actual number. If the number of beans in the jar is 645, which equation can be used to find the minimum and maximum number of beans that will win the contest, and what is the maximum guess that could win?

A
|x – 645| = 20; maximum guess: 635 beans
B
|x – 645| = 20; maximum guess: 665 beans
C
|x – 20| = 645; maximum guess: 635 beans
D
|x – 20| = 645; maximum guess: 665 beans
5

Sharon’s turtle escaped from her backyard sometime in the last few hours. According to her calculations, the farthest the turtle could have gone is 4 blocks down the road in either direction. If Sharon lives on the 112th block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?

A
|x – 112| = 0
B
|x – 112| = 4
C
|4 – 112| = x
D
|112 – 4| = x
6

Which statement is true?

A
The equation –3|2x + 1.2| = –1 has no solution.
B
The equation 3.5|6x – 2| = 3.5 has one solution.
C
The equation 5|–3.1x + 6.9| = –3.5 has two solutions.
D
The equation –0.3|3 + 8x| = 0.9 has no solution.
7

Which equation has no solution?

A
|–x – 3| = 5
B
|2x – 1| = 0
C
|5 – 3x| = –8
D
|–x + 9| = 0
8

For water to be a liquid, its temperature must be within 50 Kelvin of 323 Kelvin. Which equation can be used to determine the minimum and maximum temperatures between which water is a liquid?

A
|323 – 50| = x
B
|323 + 50| = x
C
|x – 323| = 50
D
|x + 323| = 50
9

Misha found that the equation –|2x – 10| – 1 = 2 had two possible solutions: x = 3.5 and x = –6.5. Which explains whether or not her solutions are correct?

A
She is correct, because both solutions satisfy the equation.
B
She is not correct, because she made a sign error.
C
She is not correct, because there are no solutions.
D
She is not correct, because there is only one solution: x = 3.5.
10

Which equation has no solution?

A
|4x – 2| = –6
B
|–2 – x| = 9
C
|3x + 6| = 6
D
|–2x + 8| = 0

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