Solving Absolute Value Equations

Savanah solved the equation 3 + 4| + 3| = 11 for one solution. Her work is shown below: 4| + 3| = 8 | + 3| = 2 + 3 = 2 = -1 x = -2 What is the other solution to the given absolute value equation?

x = -10

Max rides his scooter toward Kim and then passes her at a constant speed. His distance in feet, d, from Kim t seconds after he started riding his scooter is given by d = |150 - 9t|. 1: What does the 150 in the equation represent? 2: What does the 9 in the equation represent?

1: Max's starting distance from Kim 2: Max's constant speed

Josefina started to solve for x in the equation 3.5 = 1.9 - 0.8|2x - 0.6| using the steps below: 3.5 = 1.9 - 0.8|2x - 0.6| 1.6 = -0.8|2x - 0.6| -2 = |2x - 0.6| Why did Josefina stop at Step 3?

Absolute values cannot equal a negative number. This equation has no solution.

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

D: The number line with one point on -4, and another point on 8.

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?

D: |x - 57| = 3

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

|x + 333.22 | =.12.78

Which statements are true for solving the equation 0.5 - |x - 12| = -0.25? Check all that apply. The equation will have no solutions. A good first step for solving the equation is to subtract 0.5 from both sides of the equation. A good first step for solving the equation is to split it into a positive case and a negative case. The positive case of this equation is 0.5 - |x - 12| = 0.25. The negative case of this equation is x - 12 = -0.75. The equation will have only 1 solution

B and E 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.

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

C: x can equal -3.2 or -7.4.

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.

A and E 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.

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. ? is the maximum temperature at which nitrogen is a liquid. ? is the minimum temperature at which nitrogen is a liquid.

-320.44 is the maximum temperature at which nitrogen is a liquid. -346 is the minimum temperature at which nitrogen is a liquid.