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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