Question

solve the following compound inequality. 18r + 6 < 24 or 7r - 9 > 12 r < ? or r >

Explanation:

Step1: Solve the first inequality

Subtract 6 from both sides of \(18r + 6<24\): \(18r+6 - 6<24 - 6\), which simplifies to \(18r<18\). Then divide both sides by 18: \(r < \frac{18}{18}\), so \(r<1\).

Step2: Solve the second inequality

Add 9 to both sides of \(7r - 9>12\): \(7r-9 + 9>12 + 9\), which simplifies to \(7r>21\). Then divide both sides by 7: \(r>\frac{21}{7}\), so \(r > 3\).

Answer:

\(r<1\) OR \(r>3\)