Question

Solve: a + 8 – 2(a – 12) > 0

Answer 1

First, distribute the -2 on the left side.
Then collect like terms.
Then add or subtract (on both sides) the number on the left side so you move it to the right side.
Next, divide both sides by the number that multiplies a.

Answer 2

a + 8 - 2(a - 12) > 0

a + 8 -2a + 24 > 0

a - 2a + 32 > 0

-a > -32

Since we are dividing by a negative number, the sign of the inequality must be reversed.

-a/-1 < -32/-1

a < 32

The value of "a" must be less than 32 to make the original inequality a true statement.

Prove:

Let a = 30


a + 8 -2(a - 12) > 0

30 + 8 -2(30 - 12) > 0

30 + 8 - 2(18) > 0

38 - 36 > 0

2 > 0 is a true statement.

Thus, the answer to your question is a < 32.