### Solve absolute Value Inequalities

```Solve absolute Value Inequalities
Isolate the absolute value on one side of the equation.
Write the problem as a compound inequality.
LESS THAN:
If absolute value is <a, then write the problem as a compound
inequality
-a< || < a
GREATER THAN:
If absolute value is > a, then write the problem as 2 inequality
problems:
|| < -a and || > a
Solve for x.
Simplify.
Check it in the ORIGINAL Equation!!
Note : When you have an “x” on both sides of the “=“,
you may get an extraneous solution.
Absolute Value Inequalities
Examples
|2x-3|<5
-5 < 2x-3 <5
-2 < 2x <8
-1 < x < 4
It on a number line.
(-1,4)
Absolute Value Inequalities
Example #2
|2x-1| >5
|2x-1| < -5
2x < -4
X < -2
| 2x-1| > 5
2x -1 > 5
2x > 6
X>3
Write your answer using proper interval notation and graph it on a number line.
(-∞, -2) U ( 3, ∞)
Absolute value inequality
Word Problems
A manufacturer has a .6 oz tolerance for a bottle of salad dressing
Write and solve an absolute value inequality that describes the acceptable
volumes for “16 oz” bottles
HINT: If you want WITHIN the range use <,
If you want OUTSIDE the range use > .
| actual amount – ideal amount| < tolerance
| x -16|< .6
-.6< x-16< .6
15.4 < X < 16.6
This means that you could actually buy a 15.4 to 16.6 oz salad dressing that
is labeled and sold as 16 oz.
Absolute Value inequality
Word Problem
A city ordinance states that pools must be enclosed by a fence that is between
3 to 6 feet high.
Write an absolute value inequality describing fences that don’t meet this
ordinance.
How do you find the tolerance?
Tolerance = (high end) – (average of low and high ends)
| actual height – average height| > tolerance
| h – [(3+6)/2] > 6-4.5
|h – 4.5| > 1.5
```