What is the solution to the compound inequality 3x-8>-5 and 2x-7<5

1 < x < 6 ⇒ x ∈ (1, 6)

Step-by-step explanation:

3x - 8 > - 5 add 8 to both sides

3x > 3 divide both sides by 3

x > 1

2x - 7 < 5 add 7 to both sides

2x < 12 divide both sides by 2

x < 6

From x > 1 and x < 6 we have the solution 1 < x < 6 ⇒ x ∈ (1, 6)