Solving Absolute Value Equations

Question 1

Which equation has no solution?

Revolt · Accepted Answer

|4x – 2| = –6

Question 2

Which equation has no solution?

Revolt · Accepted Answer

|5 – 3x| = –8

Question 3

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 4

Which statement is true?

Revolt · Accepted Answer

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

Question 5

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 6

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

Revolt · Accepted Answer

x = 0 or x = 6

Question 7

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 8

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

Revolt · Accepted Answer

x = 0 or x = 3

Question 9

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 10

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?

Revolt · Accepted Answer

|x – 645| = 20; maximum guess: 665 beans

Solving Absolute Value Equations Answers

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