### About Solving Absolute Value Equations:

The absolute value of a number is the distance between the number and zero on the number line. Opposites are numbers that have the same absolute value, for example (5, and -5). When we solve an absolute value equation such as |x| = 5, there are two solutions: x = 5 or x = -5.

Test Objectives

- Demonstrate a general understanding of absolute value
- Demonstrate the ability to solve a compound equation with "or"
- Demonstrate the ability to solve an absolute value equation

#1:

Instructions: Solve each equation.

a) -9|8 + 6x| - 7 = -25

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#2:

Instructions: Solve each equation.

a) -10|5n + 6| - 5 = -5

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#3:

Instructions: Solve each equation.

a) 3|-10 + 5p| + 1 = 106

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#4:

Instructions: Solve each equation.

a) 5 + 9|5p - 4| = -31

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#5:

Instructions: Solve each equation.

a) |x + 4| = |5x + 8|

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Written Solutions:

#1:

Solutions:

a) $$x = -1$$ or $$x = -\frac{5}{3}$$

$$\left\{-1,-\frac{5}{3}\right\}$$

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#2:

Solutions:

a) $$n = -\frac{6}{5}$$

$$\left\{-\frac{6}{5}\right\}$$

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#3:

Solutions:

a) $$p = 9$$ or $$p = -5$$

{-5,9}

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#4:

Solutions:

a) No solution: ∅

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#5:

Solutions:

a) $$x = -1$$ or $$x = -2$$

{-2,-1}