# 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 2|(2x)/3 + 1|>=4

### 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

1. Solve  |5 − x| ≤ 2

2. Solve |(2x-9)/4|<1

3. Solve |(4x)/3-5|>=7

4. Solve |x^2+3x-1|<3

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