Solving Absolute Value Equations

Question 1

Which equation has no solution?

Revolt · Accepted Answer

|5 – 3x| = –8

Question 2

Which statement is true?

Revolt · Accepted Answer

The equation –0.3|3 + 8x| = 0.9 has no solution.

Question 3

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

Revolt · Accepted Answer

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

Question 4

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

Revolt · Accepted Answer

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

Question 5

Which equation has no solution?

Revolt · Accepted Answer

|4x – 2| = –6

Question 6

Which equation has only one solution?

Revolt · Accepted Answer

|–6x + 3| = 0

Question 7

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?

Revolt · Accepted Answer

492 meters and 508 meters

Question 8

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?

Revolt · Accepted Answer

|x – 112| = 4

Question 9

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

Revolt · Accepted Answer

x=−4

Question 10

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

Revolt · Accepted Answer

x = 0 or x = 3

Solving Absolute Value Equations Answers

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