To solve absolute value inequalities: 1) Simplify any terms outside the absolute value bars first, then remove the bars to treat the expression normally. 2) Solve the simplified inequality like a normal equation, then check solutions by substituting back into the absolute value bars. 3) Perform the "negative variation" by changing the sign of numbers inside the bars and re-solving to find all solutions.

1. How to Solve Absolute
Value Inequalities

2. If there is any number outside
the absolute value equation,
solve that first.
When you are done with that,
you take the equation out of
the bars

3. Now solve like
normal

4. To check, you put the
equation back in the
absolute value bars.

5. And now do the
Negative Variation.

6. And solve it the same
way…

7. UNTIL YOU GET
TO THE CHECK
Put it back to the absolute
value bars, but make the
negative number positive
again.

8. And you have your
solution!

9. Notes
If the absolute value equation is equal to zero, then it has one solution
If the absolute value equation is equal to a negative number, then there is no
solution.