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