B
1‐5B: Absolute Value Inequalities
Objectives:
• To solve absolute value inequalities.
• To graph absolute value inequalities.
• To consider "special cases" of absolute value inequalities.
Developing the "rule"
THINK ABOUT IT...
If , then is more than 3 units away from 0 on the number line in either a positive or a negative direction. What will the graph look like?
0
Developing the "rule"
THINK ABOUT IT...
If , then is less than 3 units away from 0 on the number line in either a positive or a negative direction. What will the graph look like?
0
When solving an inequality with an absolute value in it,
follow these steps...
1. isolate the absolute value (add, subtract, multiply or divide away numbers that are outside of the absolute value... NEVER distribute into absolute value!!)
2. set up a positive case and a negative case and choose the appropriate conjunction ("and" if >, "or" if < )
3. solve both cases
4. graph the two "rough draft" solutions below the number line 5. shade the "final copy" solutions on the number line 6. check your shading by picking 3 "test" points (one from each section of the number line) and plug them into the original inequality
Please follow these notes, not what the textbook shows...
EX #1:
Practice Problem:
Remember to get the absolute value ALONE first, then do a + case and a ­ case.
Also, NEVER, NEVER, NEVER distribute into an absolute value!!!
EX #2:
Practice Problem:
EX #3:
"Special" Cases