Question

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

Answer 1

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

Answer 2

Answer:

5<x<8

Step-by-step 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