Question

a compound inequality is shown:
-3x + 11 ≥ 20 or \frac{1}{2}x - 7 > -5
which graph represents the solution set of the compound inequality?

Explanation:

Step1: Solve the first inequality

Solve \(-3x + 11\geq20\).
Subtract \(11\) from both sides: \(-3x\geq20 - 11\), so \(-3x\geq9\).
Divide both sides by \(-3\) (and reverse the inequality sign): \(x\leq - 3\).

Step2: Solve the second inequality

Solve \(\frac{1}{2}x-7>-5\).
Add \(7\) to both sides: \(\frac{1}{2}x>-5 + 7\), so \(\frac{1}{2}x>2\).
Multiply both sides by \(2\): \(x>4\).

Answer:

The solution set is \(x\leq - 3\) or \(x>4\). The graph with a closed circle at \(-3\) (since \(x = - 3\) is included in \(x\leq - 3\)) and an arrow to the left, and an open circle at \(4\) (since \(x = 4\) is not included in \(x>4\)) and an arrow to the right. Looking at the options, the second option (with a closed circle at \(-3\) and an open circle at \(4\)) is correct.