Answer :
Answer:
A.
Step-by-step explanation:
We are told that three that the sum of 5 and a number is between 12 and 21 which means:
[tex]12<3(x+5)<21[/tex]
Divide all sides by 3:
[tex]\frac{12}{3}<\frac{3(x+5)}{3}<\frac{21}{3}[/tex]
[tex]4<(x+5)<7[/tex]
[tex]4<x+5<7[/tex]
Subtract 5 on both sides:
[tex]4-5<x<7-5[/tex]
Simplify:
[tex]-1<x<2[/tex]
So the answer is A.
Slightly different route:
[tex]12<3(x+5)<21[/tex]
Distribute 3 to the terms in the ( ) next to it:
[tex]12<3x+15<21[/tex]
Subtract all sides by 15:
[tex]12-15<3x<21-15[/tex]
Simplify:
[tex]-3<3x<6[/tex]
Divide both sides by 3:
[tex]\frac{-3}{3}<\frac{3x}{3}<\frac{6}{3}[/tex]
Simplify:
[tex]-1<x<2[/tex]