Solving Absolute Value Equations

Question 1

Which number line represents the solutions to |x – 2| = 6?

Revolt · Accepted Answer

D:

Question 2

Jamaal is allowed to walk no farther than three blocks in either direction from his house. If his house is located on the 57th block of the town, which absolute value equation can be used to determine the farthest block to which Jamaal is allowed to walk?

Revolt · Accepted Answer

D: |x – 57| = 3

Question 3

What value or values of x satisfy 2|x + 5.3| = 4.2?

Revolt · Accepted Answer

C: x can equal –3.2 or –7.4.

Question 4

Which statements are true? Check all that apply.The equation |–x – 4| = 8 will have two solutions.The equation 3.4|0.5x – 42.1| = –20.6 will have one solution.The equation = 0 will have no solutions.The equation |2x – 10| = –20 will have two solutions.The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.The equation = 5 will have infinitely many solutions.

Revolt · Accepted Answer

A: The equation |–x – 4| = 8 will have two solutions.; E: The equation |0.5x – 0.75| + 4.6 = 0.25 will have no solutions.

Question 5

x = [___]

Revolt · Accepted Answer

-3

Question 6

Question 6

Revolt · Accepted Answer

B: A good first step for solving the equation is to subtract 0.5 from both sides of the equation.; E: The negative case of this equation is x – 12 = –0.75.

Question 7

Question 7

Revolt · Accepted Answer

A

Question 8

Sample Respnse: Josefina saw that the absolute value was equal to a negative value. Since absolute values represent distances from values, they cannot be negative. Therefore, she knew there was no viable answer.

Revolt · Accepted Answer

Josefina is correct. When she subtracts 5 from both sides of the equation |x + 2| + 5 = 2, she gets |x + 2| = -3. Since an absolute value represents distance from zero and must be non-negative, the absolute value of an expression can never be equal to a negative number. Therefore, the equation has no solution.

Question 9

[___]

Revolt · Accepted Answer

A: Max’s starting distance from Kim

Question 10

For nitrogen to be a liquid, its temperature must be within 12.78 °F of –333.22 °F. The equation |x + 333.22 | = 12.78 can be used to find x, which represents the maximum and minimum temperatures at which nitrogen is a liquid.

Revolt · Accepted Answer

: -320.44; : -346

Solving Absolute Value Equations Answers

More from this Course

TRY EDGENUITY HACKS