Answer:
The solution for the compound inequality = ∅
Step-by-step explanation:
The given inequality:
3x - 8 ≤ -5  &  2x - 7 > 5
<u>For the inequality 3x - 8 ≤ -5</u>
3x - 8 ≤ -5    add 8 to both sides
3x  ≤ 3          divide both side by 3
x  ≤ 1
So, the solution of the inequality 3x - 8 ≤ -5 ⇒ x ∈ (-∞ , 1]
<u>For the inequality 2x - 7 > 5</u>
2x - 7 > 5      add 7 to both sides
2x > 12          divide both sides 2
x > 6
So, the solution of the inequality 2x - 7 > 5 ⇒ x ∈ (6 , ∞)
The solution for the compound inequality will be:
(-∞ , 1] ∩ (6 , ∞) = ∅
See the attached figure.