write the answer in interval notation

Question

|12-5x|<22  solve and check the inequality.

Answer 1

The inequality is |12 - 5x | < 22.

Write |12 - 5x | < 22 as (12 - 5x ) < 22 and (12 - 5x ) > - 22

Case 1 : (12 - 5x ) is positive.

(12 - 5x ) < 22

Subtract 12 from each side.

- 5x < 22 - 12

- 5x < 10

Divide each side by negative 5 and flip the symbol.

x > - 10/5

x > - 2.

Case 2 : (12 - 5x ) is negative.

- (12 - 5x ) < 22

Multiply each side by negative 1 and flip the symbol.

(12 - 5x ) > - 22

Subtract 12 from each side.

- 5x > -22 - 12

- 5x > - 34

Divide each side by negative 5 and flip the symbol.

x < 34/5.

Solution set is {x | - 2 < x < 34/5}.