solve and graph 3x-6>-18 and 4x-5<3

Question

need help solving a graph written out and graphed. 3x-6>-18 and 4x-5<3

Answer 1

The compound inequality is 3x - 6 > - 18 and 4x - 5 < 3.

Solve the inequality 1 : 3x - 6 > - 18 for x.

Add 6 to each side.

3x - 6 + 6 > - 18 + 6

3x > - 12

Divide each side by 3.

3x/3 > - 12/3

x > - 4.

 

Solve the inequality 2 : 4x - 5 < 3 for x.

Add 5 to each side.

4x - 5 + 5 < 3 + 5

4x < 8

Divide each side by 4.

4x/4 < 8/4

x < 2.

The solution of the compound inequality is x > - 4 and x < 2 or -4 < x < 2.

 

Solution set of the inequality is {x | -4 < x < 2}.

Graph the solution set on a number line.

 

Note : A circle means that the points -4 and 2 are not included in the solution set.