Question

solve the compound inequality. state the solution set as an interval. if there is no solution, type dne in the answer box. -3x - 5 > 4 and 3x - 3 ≥ 12 the solution set as an interval is:

Explanation:

Step1: Solve \(-3x - 5 > 4\)

Add 5 to both sides: \(-3x - 5 + 5 > 4 + 5\)
Simplify: \(-3x > 9\)
Divide both sides by -3 (reverse inequality): \(x < -3\)

Step2: Solve \(3x - 3 \geq 12\)

Add 3 to both sides: \(3x - 3 + 3 \geq 12 + 3\)
Simplify: \(3x \geq 15\)
Divide by 3: \(x \geq 5\)

Step3: Find intersection

The first inequality gives \(x < -3\), the second gives \(x \geq 5\). No overlap, so no solution.

Answer:

DNE