Question

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

Answer 1

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.