Solving Absolute Value Equations

Question 1

Which equation has only one solution?

Revolt · Accepted Answer

|–6x + 3| = 0

Question 2

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

Revolt · Accepted Answer

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

Question 3

Which statement is true?

Revolt · Accepted Answer

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

Question 4

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?

Revolt · Accepted Answer

|x – 42.80| = 12

Question 5

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?

Revolt · Accepted Answer

She is not correct, because there are no solutions.

Question 6

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 7

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

Revolt · Accepted Answer

x = 0 or x = 3

Question 8

Which equation has no solution?

Revolt · Accepted Answer

|4x – 2| = –6

Question 9

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

Revolt · Accepted Answer

x = 0 or x = 6

Question 10

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

Solving Absolute Value Equations Answers

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