Solving Absolute Value Equations and Inequalities

Your Notes
Example 2
Solving an Inequality of the form⏐ax b⏐ < c
Solve ⏐2x 3⏐ < 3.
Solution
⏐2x 3⏐ < 3 Write original inequality.
3 < 2x 3 < 3 Write equivalent compound inequality.
0 < 2x < 6 Add 3 to each expression.
0 < x < 3 Divide each expression by 2 .
The solutions are all real numbers greater than 0 and less
than 3 . Check several solutions in the original inequality.
Graph the solution below.
2 1
0 1 2 3 4 5
Example 3
Solving an Inequality of the form ⏐ax b⏐ ≥ c
Solve ⏐2x 7⏐ ≥ 3.
Solution
This absolute value inequality is equivalent to 2x 7 ≤ 3
or 2x 7 ≥ 3 .
Solve first inequality
Solve second inequality
2x 7 ≤ 3 Write inequality. 2x 7 ≥ 3
2x ≤ 10 Subtract 7 2x ≥ 4
from each side.
x ≤ 5 Divide each side x ≥ 2
by 2 .
The solutions are all real numbers less than or equal to 5
or greater than or equal to 2 . Check several solutions in
the original inequality. Graph the solution below.
7
6 5
4 3 2 1
0
Lesson 1.7 • Algebra 2 Notetaking Guide 23