### 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 Practice Test:

#1:

Instructions: solve each equation.

$$a)\hspace{.2em}|x + 6|=1$$

$$b)\hspace{.2em}|x + 2|=8$$

#2:

Instructions: solve each equation.

$$a)\hspace{.2em}|9x + 9|=|2x - 6|$$

$$b)\hspace{.2em}|4 - 7x|=|-x + 4|$$

#3:

Instructions: solve each equation.

$$a)\hspace{.2em}8 - 7|9x - 2|=-6$$

$$b)\hspace{.2em}6|10x - 1| - 4=50$$

#4:

Instructions: solve each equation.

$$a)\hspace{.2em}9 + 2|3x + 7|=-37$$

$$b)\hspace{.2em}4|-3 - 8x| + 2=118$$

#5:

Instructions: solve each equation.

$$a)\hspace{.2em}-\frac{11}{10}\left|\frac{3}{2}x + \frac{5}{2}\right| + \frac{4}{5}=-\frac{147}{160}$$

$$b)\hspace{.2em}-\frac{4}{5}\left|\frac{3}{2}x - \frac{28}{9}\right| + \frac{8}{5}=\frac{14}{45}$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}x=-7,-5$$

$$b)\hspace{.2em}x=-10,6$$

#2:

Solutions:

$$a)\hspace{.2em}x=-\frac{15}{7}, -\frac{3}{11}$$

$$b)\hspace{.2em}x=0,1$$

#3:

Solutions:

$$a)\hspace{.2em}x=0, \frac{4}{9}$$

$$b)\hspace{.2em}x=-\frac{4}{5}, 1$$

#4:

Solutions:

$$a)\hspace{.2em}No \hspace{.2em}Solution$$

$$b)\hspace{.2em}-4, \frac{13}{4}$$

#5:

Solutions:

$$a)\hspace{.2em}x=-\frac{5}{8}, -\frac{65}{24}$$

$$b)\hspace{.2em}x=1, \frac{85}{27}$$