Given A = {18, 6, - 3, - 12} Determine all elements of set A that are in the solution of the inequality 2/3x + 3 < - 2x - 7

Plug in each value in the set into x, and evaluate both sides.

The values of x that make the inequality true are the answer.

Start with 18.

2/3x + 3 < - 2x - 7

2/3 (18) + 3 < - 2 (18) - 7

12 + 3 < - 36 - 7

15 < - 43 is false, so 18 does not work.

Now do 6.

2/3x + 3 < - 2x - 7

2/3 (6) + 3 < - 2 (6) - 7

4 + 3 < - 12 - 7

7 < - 19 is false, so 6 does not work.

Now do - 3.

2/3x + 3 < - 2x - 7

2/3 (-3) + 3 < - 2 (-3) - 7

-2 + 3 < 6 - 7

1 < - 1 is false, so - 3 does not work.

Now do - 12.

2/3x + 3 < - 2x - 7

2/3 (-12) + 3 < - 2 (-12) - 7

-8 + 3 < 24 - 7

-5 < 17 is true, so - 12 does not work.