Question

What is the solution to the compound inequality 3x-8 less than or equal to -5 or 2x - 7 > 5

Answer 1

The solution for the compound inequality = ∅

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.