Questions: Solve the compound inequality and give your answer in interval notation. 4x+6<-22 OR -5x-6 ≤ 9

Solution Steps

To solve the compound inequality, we need to solve each inequality separately and then combine the solutions. The first inequality is \(4x + 6 < -22\), and the second inequality is \(-5x - 6 \leq 9\). For the "OR" condition, we take the union of the solution sets of the two inequalities.

The first inequality is \(4x + 6 < -22\). To solve for \(x\), we first subtract 6 from both sides:

\[ 4x < -28 \]

Next, divide both sides by 4:

\[ x < -7 \]

The second inequality is \(-5x - 6 \leq 9\). To solve for \(x\), add 6 to both sides:

\[ -5x \leq 15 \]

Then, divide both sides by -5, remembering to reverse the inequality sign:

\[ x \geq -3 \]

The compound inequality is connected by "OR", so we take the union of the solution sets. The solutions are:

• From the first inequality: \(x < -7\)
• From the second inequality: \(x \geq -3\)

The combined solution in interval notation is:

\[ (-\infty, -7) \cup [-3, \infty) \]

Final Answer