Solve & write answer in Interval Notation:

Question

I 5x + 2 I ≤ 13?

Answer 1

The inequality is |5x + 2 | ≤ 13.

Write |5x + 2 | ≤ 13 as (5x + 2) ≤ 13 and (5x + 2) ≥ 13.

Case 1 : (5x + 2) is positive.

(5x + 2) ≤ 13

5x ≤ 13 - 2

5x ≤ 11

x ≤ 11/5.

Case 2 : (5x + 2) is negative.

- (5x + 2 ) ≤ 13

Multiply each side by negative 1 and flip the symbol.

(5x + 2 ) ≥ - 13

5x ≥ - 13 - 2

5x ≥ - 15

x ≥ - 15/5

x ≥ - 3.

Solution set is {x | - 3 ≤ x ≤ 11/5}.

The solution in interval notation is [- 3, 11/5].