AnswersAlgebra 1Solving Absolute Value Equations

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What is the solution to negative 2 start absolute value 2 point 2 x minus 3 point 3 end absolute value is equal to negative 6 point 6 ?

A
x is equal to 0 or x is equal to 3
B
x is equal to 3
C
x is equal to negative 3 or x is equal to 0
D
x is equal to negative 3
3

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 one hundred and twelfth block of town, which equation can be used to find the block numbers that represent the farthest distance that the turtle may be?

A
start absolute value x minus 112 end absolute value is equal to 0
B
start absolute value x minus 112 end absolute value is equal to 4
C
start absolute value 112 minus 4 end absolute value is equal to x
D
start absolute value 4 minus 112 end absolute value is equal to x
4

Which equation has no solution?

A
start absolute value negative x minus 3 end absolute value is equal to 5
B
start absolute value 2 x minus 1 end absolute value is equal to 0
C
start absolute value negative x plus 9 end absolute value is equal to 0
D
start absolute value 5 minus 3 x end absolute value is equal to negative 8
5

Which number line represents the solutions to absolute value of x plus 4 is equal to 2 ?

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

A while back, either James borrowed 12 dollars from his friend Rita or she borrowed 12 dollars from him, but he can’t quite remember which. Either way, he is planning to pay her back or ask that she pay him back this afternoon. If he has 42 point 8 0 dollars in his wallet, which equation represents the amount of money he may have after he sees Rita?

A
start absolute value x plus 42 point 8 0 end absolute value is equal to 12
B
start absolute value x plus 12 end absolute value is equal to 42 point 8 0
C
start absolute value x minus 42 point 8 0 end absolute value is equal to 12
D
start absolute value x minus 12 end absolute value is equal to 42 point 8 0
7

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
start absolute value x minus 645 end absolute value is equal to 20 ; maximum guess: 665 beans
B
start absolute value x minus 20 end absolute value is equal to 645 ; maximum guess: 665 beans
C
start absolute value x minus 20 end absolute value is equal to 645 ; maximum guess: 635 beans
D
start absolute value x minus 645 end absolute value is equal to 20 ; maximum guess: 635 beans
8

Misha found that the equation negative start absolute value 2 x minus 10 end absolute value minus 1 is equal to 2 had two possible solutions: x is equal to 3 point 5 and x is equal to negative 6 point 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 there are no solutions.
C
She is not correct because there is only one solution: x is equal to 3 point 5 .
D
She is not correct because she made a sign error.
9

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
start absolute value x plus 323 end absolute value is equal to 50
B
start absolute value x minus 323 end absolute value is equal to 50
C
start absolute value 323 plus 50 end absolute value is equal to x
D
start absolute value 323 minus 50 end absolute value is equal to x
10

Which statement is true?

A
The equation negative 3 start absolute value 2 x plus 1 point 2 end absolute value is equal to negative 1 has no solution.
B
The equation negative 0 point 3 start absolute value 3 plus 8 x end absolute value is equal to 0 point 9 has no solution.
C
The equation 3 point 5 start absolute value 6 x minus 2 end absolute value is equal to 3 point 5 has one solution.
D
The equation 5 start absolute value negative 3 point 1 x plus 6 point 9 end absolute value is equal to negative 3 point 5 has two solutions.

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