Question

how to solve this inequality |1 - 6x | - 6 < -3.

Answer 1

The inequality is |1 - 6x | -6 < -3.

Add 6 to each side.

|1 - 6x | -6 + 6< -3 + 6

|1 - 6x | < 3.

The absolute value inequality |1 - 6x | < 3 is equivalent to -3 < 1 - 6x < 3.

Solve the inequality -3 < 1 - 6x < 3.

Subtract 1 from each part.

-3 -1 < 1 - 6x -1 < 3 -1

-4 < - 6x < 2

Divide each part by negative 6 and reverse the inequality symbol.

-4/-6 > - 6x/-6 > 2/-6

2/3 > x > -1/3

The solution set is { x | -1/3 < x < 2/3 }.