# Linear Inequations-9

### From Homeworkwiki

**Find the solution set of the inequation |3x - 2|≤ 1/2**

**Solution:** We know that

|x - a| ≤ r <=> a – r ≤ x ≤ a + r

|3x - 2|≤ 1/2 <=> 2 – 1/2 ≤ 3x ≤ 2 + 1/2

<=> 3/2 ≤ 3x ≤ 5/2

<=> 1/2 ≤ x ≤ 5/6

<=> x ∈ [1/2, 5/6]

Hence, the solution set of the given inequation is the interval [1/2, 5/6]