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
#2:
Instructions: Solve each equation.
a) -10|5n + 6| - 5 = -5
#3:
Instructions: Solve each equation.
a) 3|-10 + 5p| + 1 = 106
#4:
Instructions: Solve each equation.
a) 5 + 9|5p - 4| = -31
#5:
Instructions: Solve each equation.
a) |x + 4| = |5x + 8|
Written Solutions:
Solution:
a) $$x = -1$$ or $$x = -\frac{5}{3}$$
$$\left\{-1,-\frac{5}{3}\right\}$$
Solution:
a) $$n = -\frac{6}{5}$$
$$\left\{-\frac{6}{5}\right\}$$
Solution:
a) $$p = 9$$ or $$p = -5$$
{-5,9}
Solution:
a) No solution: ∅
Solution:
a) $$x = -1$$ or $$x = -2$$
{-2,-1}