# 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 |2*x* − 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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