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Absolute Value Equations Test
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

Solving Absolute Value Equations Test:




#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:


Solution:


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


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


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#2:


Solution:


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


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


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#3:


Solution:


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


{-5,9}


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#4:


Solution:


a) No solution: ∅


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#5:


Solution:


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


{-2,-1}


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