# Linear Inequations-12

### From Homeworkwiki

**Solve the following system of inequations:**

**|x - 1| ≤ 5, |x| ≥ 2**

**Solution:** The given system of inequations is

|x - 1| ≤ 5 --------------------------------------(i)

|x| ≥ 2-------------------------------------------(ii)

Now, |x - 1| ≤ 5 => 1 – 5 ≤ x ≤ 1 + 5 [since, |x - a| ≤ r <=> a – r ≤ x ≤ a + 1]

=>-4 ≤ x ≤ 6

=> x ∈ [-4, 6]

Thus, the solution set of (i) is the interval x ∈ [-4, 6]

and, |x| ≤ 2 => x ≤ -2, or x ≥ 2

=>x ∈ (-∞, -2] U [2, ∞)

Thus, the solution set of (ii) is (-∞, -2] U [2, ∞)

Hence, the solution set of the given system of inequations is [-4, -2] U [2, 6].