Answer:
The solution for the compound inequality = ∅
Step-by-step explanation:
The given inequality:
3x - 8 ≤ -5 & 2x - 7 > 5
For the inequality 3x - 8 ≤ -5
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]
For the inequality 2x - 7 > 5
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.
