The compound inequality is:
x ≥ 16/5 and x ≤ -3/4
The correct option is D, because there is no solution for this inequality.
How to solve the inequality?
Here we have a compound inequality:
5x - 4 ≥ 12 AND 12x + 5 ≤ -4
We need to isolate x in both inequaltities, for the first one:
5x - 4 ≥ 12
5x ≥ 12 + 4
5x ≥ 16
x ≥ 16/5
For the second:
12x + 5 ≤ -4
12x ≤ -4 - 5
12x ≤ -9
x ≤ -9/12
x ≤ -3/4
Then the compound inequality is:
x ≥ 16/5 and x ≤ -3/4
This can't be true, so there is no solution.