Question

1. 12a + 12 < 84 and -10a - 7 ≤ 63

Explanation:

Step1: Solve \(12a + 12 < 84\)

Subtract 12 from both sides: \(12a + 12 - 12 < 84 - 12\)
Simplify: \(12a < 72\)
Divide both sides by 12: \(\frac{12a}{12} < \frac{72}{12}\)
Simplify: \(a < 6\)

Step2: Solve \(-10a - 7 \leq 63\)

Add 7 to both sides: \(-10a - 7 + 7 \leq 63 + 7\)
Simplify: \(-10a \leq 70\)
Divide both sides by -10 (remember to reverse the inequality sign): \(\frac{-10a}{-10} \geq \frac{70}{-10}\)
Simplify: \(a \geq -7\)

Step3: Find the intersection of the two solutions

We have \(a < 6\) and \(a \geq -7\), so the solution is \(-7 \leq a < 6\)

Answer:

The solution to the compound inequality is \(-7 \leq a < 6\)