Question

a) x - 4 < -7 or 2x ≥ 12

Explanation:

Step1: Solve \( x - 4 < -7 \)

Add 4 to both sides of the inequality:
\( x - 4 + 4 < -7 + 4 \)
\( x < -3 \)

Step2: Solve \( 2x \geq 12 \)

Divide both sides by 2:
\( \frac{2x}{2} \geq \frac{12}{2} \)
\( x \geq 6 \)

Step3: Combine the solutions (OR)

The solution to the compound inequality \( x - 4 < -7 \) OR \( 2x \geq 12 \) is the union of the solutions to each inequality. So we have \( x < -3 \) or \( x \geq 6 \).

Answer:

The solution is \( x < -3 \) or \( x \geq 6 \)