Question

Which graph represents the solution set of the compound inequality below? x + 3 < (4x – 12) < 20

Answer 1

5<x<8

Explanation:

x + 3 < (4x – 12) < 20

Solve the inequality

x + 3 < 4x – 12 < 20

We break the inequality

x+3<4x-12 and 4x-12<20

solve it separately

x+3<4x-12

subtract 4x on both sides

-3x +3< -12

subtract 3 on both sides

-3x < -15

divide by -3 on both sides

x> 5

4x-12<20

add 12 on both sides

4x <32

divide by 4

x<8

x>5 and x<8

so x lies between 5 and 8, 5<x<8

the graph is attached below

Answer 2

x + 3 < 4x - 12 or 4x - 12 < 20

-x -x +12 +12

3 < 3x - 12 or 4x < 32

+12 +12 ÷4 ÷4

15 < 3x or x < 8

÷3 ÷3

5 < x

5 < x < 8

Graph: 5 o---------------o 8