Question

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

Answer 1

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

4x > -4 8x < -8

x > -1 x < -1

So we have x ≠ -1.

Answer 2

To solve the given inequalities, you can isolate the variable x by performing the same operation on both sides. For the first inequality, adding 39 to both sides and then dividing by 4 gives x > -1. For the second inequality, subtracting 31 from both sides and dividing by 8 gives x < -1. Combining the solutions, we find -1 < x < 1.

Step-by-step explanation:

To solve the inequality 4x - 39 > -43, we can add 39 to both sides to isolate the variable:
4x > -43 + 39
Which simplifies to:
4x > -4
Now, we can divide both sides by 4 to solve for x:
x > -1

Similarly, to solve the inequality 8x + 31 < 23, we can subtract 31 from both sides:
8x < 23 - 31
Which simplifies to:
8x < -8
Now, divide both sides by 8 to solve for x:
x < -1

Combining the two solutions, we find that -1 < x < 1.