Which best describes the solution set for the inequality below?

3x + 7 ≤ 4x - 8 or - 2x + 3 ≥ 1

3x + 7 <_ 4x - 8

Subtract 3x from both sides.

3x - 3x = 0x

4x - 3x = 1x (or just x)

7 <_ x - 8

Add 8 to both sides.

7 + 8 = 15

-8 + 8 = 0

x _> 15 is the solution for the first inequality.

Although A.) is the only one with x_>15, let's continue to ensure our answer.

-2x + 3 _> 1

Subtract 3 from both sides.

3 - 3 = 0

1 - 3 = - 2

-2x _> - 2

Divide both sides by - 2 to solve for x.

-2x / - 2 = x

-2 / - 2 = 1

Remember to flip the inequality when dividing or multiplying by a negative.

x <_ 1 is our other inequality.

Our answers are:

x_> 15 and x<_1