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yKpoI14uk [10]
3 years ago
6

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

Mathematics
2 answers:
nordsb [41]3 years ago
6 0

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

<u>-x      </u>   <u> -x         </u>                              <u>     +12 </u>  <u>+12 </u>

     3 < 3x - 12                 or           4x        < 32

<u>    +12</u>   <u>     +12  </u>                            <u> ÷4        </u>   <u>÷4  </u>

    15 < 3x                       or              x        <  8

<u>    ÷3</u>    <u>÷3 </u>

    5 <  x

5 < x < 8

Graph:   5 o---------------o 8



Harlamova29_29 [7]3 years ago
3 0

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

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