Question

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

Answer 1

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.