4. Solving Inequalities with Absolute Values
For inequalities involving absolute values ie. |x|, we use the following relationships, for some number n:
If |f(x)| > n, then f(x) < -n or f(x) > n
If |f(x)| < n, then -n < f(x) < n
Example 1
Solve the inequality |x − 3| < 2.
Example 2
Solve the inequality |2x − 1| > 5
Example 3
Solve the inequality 
Example 4
Solve the inequality |3 − 2x| <3
Example 5
A technician measures an electric current which is 0.036 A with a possible error of ±0.002 A. Write this current, i, as an inequality with absolute values.
Exercises. Solve the given inequalities
1. Solve |5 − x| ≤ 2
2. Solve 
3. Solve 
4. Solve 
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