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}