Solving Absolute Value Equations Answers

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.

B

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

C

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 5 and one at 1.

D

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 1 and one at 5.

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.

B

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 4.

C

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 6.

D

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 4 and one at negative 2.

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.

B

A number line from negative 10 to 10 in increments of 2. Two points, one at negative 2 and one at 4.

C

A number line from negative 10 to 10 in increments of 2. Two points, one at negative 2 and one at 2.

D

A number line from negative 10 to 10 in increments of 2. Two points, one at negative 8 and one at 8.

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

11

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.

12

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.

13

Which equation has no solution?

A

|4x – 2| = –6

B

|–2 – x| = 9

C

|3x + 6| = 6

D

|–2x + 8| = 0

14

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

15

What is the solution to –4|–2x + 6| = –24?

A

x = 0

B

x = 0 or x = –6

C

x = 0 or x = 6

D

no solution

16

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

17

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.

B

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 4.

C

A number line from negative 7 to 7 in increments of 1. Two points, one at 2 and one at 6.

D

A number line from negative 7 to 7 in increments of 1. Two points, one at negative 4 and one at negative 2.

18

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

19

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

20

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

Solving Absolute Value Equations Answers

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