solve and graph absolute value funtions

Question

|15-3x|>3 I have to solve and graph this equation.

Answer 1

The inequality is |15 - 3x | > 3.

The absolute value inequality  |15 - 3x | > 3 is equivalent to 15 - 3x > 3 or 15 - 3x < -3.

Solve the inequality 1: 15 - 3x > 3.

Subtract 15 from each side.

15 - 3x - 15 > 3 -15

 - 3x > -12

Divide each side by negative 3 and reverse the inequality symbol.

 - 3x/-3 < -12/-3

Cancel common terms.

x < 4.

Solve the inequality 2:15 - 3x < -3.

Subtract 15 from each side.

15 - 3x -15 < -3 -15

 - 3x < -18

Divide each side by negative 3 and reverse the inequality symbol.

 - 3x/-3 > -18/-3

Cancel common terms.

x > 6.

The solution set is {x | x < 4 or x > 6}.

Graph the solution set for each inequality and find their intersection.

Observe the graph, the open circle means that 4 and 6 does not solutions of the inequality.