Question

Solve for x: 4x - 39 > -43 and 8x + 31 < 23

a) x > 1; x < -4
b) x < 1; x > -4
c) x > 1; x > -4
d) x < 1; x < -4

Answer 1

To solve the given inequalities, we can start by isolating x in each inequality. For the first inequality, we get x > -1 and for the second inequality, we get x < -1. Combining both solutions, the correct answer is d) x < 1 and x < -4.

Step-by-step explanation:

To solve the inequalities 4x - 39 > -43 and 8x + 31 < 23, we need to isolate x. Let's start with the first inequality:

1. Add 39 to both sides: 4x - 39 + 39 > -43 + 39
2. Simplify: 4x > -4
3. Divide by 4: x > -1

Now let's solve the second inequality:

1. Subtract 31 from both sides: 8x + 31 - 31 < 23 - 31
2. Simplify: 8x < -8
3. Divide by 8: x < -1

Combining both solutions, we have x > -1 and x < -1. Therefore, the correct answer is d) x < 1; x < -4.