Question

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 1

A.

Explanation:

We are told that three that the sum of 5 and a number is between 12 and 21 which means:

`12<3(x+5)<21`

Divide all sides by 3:

`(12)/(3)<(3(x+5))/(3)<(21)/(3)`

`4<(x+5)<7`

`4<x+5<7`

Subtract 5 on both sides:

`4-5<x<7-5`

Simplify:

`-1<x<2`

So the answer is A.

Slightly different route:

`12<3(x+5)<21`

Distribute 3 to the terms in the ( ) next to it:

`12<3x+15<21`

Subtract all sides by 15:

`12-15<3x<21-15`

Simplify:

`-3<3x<6`

Divide both sides by 3:

`(-3)/(3)<(3x)/(3)<(6)/(3)`

Simplify:

`-1<x<2`