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Three times the sum of 5 and a number is a value between 12 and 21.
Which statement best describes the number?
A. –1 < x < 2
B. x < –3 or x > 6
C. x < –1 or x > 2
D. –3 < x < 6

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]

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