Answer:
x > -1 or x < -1
Step-by-step explanation:
For the first inequality, 5x - 29 > -34:
Step 1: Add 29 to both sides to isolate the term with x
5x > -34 + 29
Step 2: Simplify the right side
5x > -5
Step 3: Divide both sides by 5
x > -1
Therefore, x must be greater than -1.
For the second inequality, 2x + 31 < 29:
Step 1: Subtract 31 from both sides
2x < 29 - 31
Step 2: Simplify the right side
2x < -2
Step 3: Divide both sides by 2
x < -1
Thus, x must be less than -1.