Question

What is the solution set for this inequality?

-8x + 40 > -16

a) x > 7

b) x < 7

c) x > -3

d) x < -3

Answer 1

The solution set for the inequality -8x + 40 > -16 is x < 7, which means option (b) x < 7 is the correct answer.

Step-by-step explanation:

To find the solution set for the inequality -8x + 40 > -16, we need to isolate the variable x.

1. Start by subtracting 40 from both sides of the inequality:
   -8x + 40 - 40 > -16 - 40, which simplifies to -8x > -56.
2. Next, divide both sides by -8, remembering that dividing by a negative number reverses the inequality sign:
   -8x / -8 < -56 / -8, which simplifies to x < 7.

Therefore, the solution to the inequality is x < 7, which corresponds to option b).