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.
$$a)\hspace{.2em}|x + 6|=1$$
$$b)\hspace{.2em}|x + 2|=8$$
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#2:
Instructions: solve each equation.
$$a)\hspace{.2em}|9x + 9|=|2x - 6|$$
$$b)\hspace{.2em}|4 - 7x|=|{-}x + 4|$$
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#3:
Instructions: solve each equation.
$$a)\hspace{.2em}8 - 7|9x - 2|=-6$$
$$b)\hspace{.2em}6|10x - 1| - 4=50$$
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#4:
Instructions: solve each equation.
$$a)\hspace{.2em}9 + 2|3x + 7|=-37$$
$$b)\hspace{.2em}4|{-}3 - 8x| + 2=118$$
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#5:
Instructions: solve each equation.
$$a)\hspace{.2em}{-}\frac{11}{10}\left|\frac{3}{2}x + \frac{5}{2}\right| + \frac{4}{5}=-\frac{147}{160}$$
$$b)\hspace{.2em}{-}\frac{4}{5}\left|\frac{3}{2}x - \frac{28}{9}\right| + \frac{8}{5}=\frac{14}{45}$$
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Written Solutions:
#1:
Solutions:
$$a)\hspace{.2em}x=-7,-5$$
$$b)\hspace{.2em}x=-10,6$$
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#2:
Solutions:
$$a)\hspace{.2em}x=-\frac{15}{7}, -\frac{3}{11}$$
$$b)\hspace{.2em}x=0,1$$
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#3:
Solutions:
$$a)\hspace{.2em}x=0, \frac{4}{9}$$
$$b)\hspace{.2em}x=-\frac{4}{5}, 1$$
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#4:
Solutions:
$$a)\hspace{.2em}\text{No Solution}$$
$$b)\hspace{.2em}{-}4, \frac{13}{4}$$
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#5:
Solutions:
$$a)\hspace{.2em}x=-\frac{5}{8}, -\frac{65}{24}$$
$$b)\hspace{.2em}x=1, \frac{85}{27}$$
