Which best describes the solution set for the inequality below?

3x + 7 ≤ 4x – 8 or –2x + 3 ≥ 1

a. x ≤ 1 or x ≥ 15
b. x ≥ 1 or x ≤ 15
c. x ≥ 1
d. x ≤ 15

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

Your answer is A.)

I hope this helps!