AnswersFL-1200310-Algebra 1 ASolving Absolute Value Equations

Solving Absolute Value Equations Answers

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Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum distances that the dog may be from the house can be found using the equation |x – 500| = 8. What are the minimum and maximum distances that Morgan’s dog may be from the house?

A
496 meters and 500 meters
B
500 meters and 508 meters
C
492 meters and 508 meters
D
496 meters and 504 meters
2
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Manuela solved the equation 3−2|0.5x+1.5|=2 for one solution. Her work is shown below.3−2|0.5x+1.5|=2 −2|0.5x+1.5|=−1 |0.5x+1.5|=0.5 0.5x+1.5=0.5 0.5x=−1 x=−2

A
x=−6
B
x=−4
C
x=2
D
x=4
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

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
5

Which equation has no solution?

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

Which number line represents the solutions to |–2x| = 4?

A
A number line from negative 10 to 10 in increments of 2. Two points, one at negative 4 and one at 2.
Option A
B
A number line from negative 10 to 10 in increments of 2. Two points, one at negative 2 and one at 4.
Option B
C
A number line from negative 10 to 10 in increments of 2. Two points, one at negative 2 and one at 2.
Option C
D
A number line from negative 10 to 10 in increments of 2. Two points, one at negative 8 and one at 8.
Option D
7

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
8

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.
9

A while back, either James borrowed $12 from his friend Rita or she borrowed $12 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 $42.80 in his wallet, which equation represents the amount of money he may have after he sees Rita?

A
|x – 42.80| = 12
B
|x + 42.80| = 12
C
|x – 12| = 42.80
D
|x + 12| = 42.80
10

Which equation has no solution?

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

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