Look at each possible solution of the inequality −12 < 2x + 8 < −6 below. Is the value of x actually a solution of the inequality? Select Yes or No for each value of x.

Question

the options that are given are

X=negative 10

X=negative 8

X=negative 14

Answer 1

Hi, Gilberto

-12< 2x + 8< -6

So, if we substitute x = -10:

2x + 8 = 2(-10) + 8 = -20 + 8 = -12

This is NOT a solution because -12 < -12 is not true.

The value of 2x + 8 has to be greater than -12.

If we substitute x = -8, then

2x + 8 = 2(-8) + 8 = -16 + 8 = -8

-12 < -8 < -6

Yes, this is true, so x = -8 IS a solution.

If we substitute x = -14:

2x + 8 = 2(-14) + 8 = -28 + 8 = -20

-12 < -20 < -6 is NOT true,

so x= -14 is NOT a solution