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 math expression

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 math expression

3. Solve math expression

4. Solve math expression

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