Question

which graph represents the compound inequality below?

$-6x - 10 < -40$ or $4x - 10 < -22$

Explanation:

Step1: Solve the first inequality

Add \(10\) to both sides of \(-6x - 10\lt - 40\):
\(-6x-10 + 10\lt -40 + 10\), so \(-6x\lt - 30\).
Divide both sides by \(-6\) (and reverse the inequality sign because we divide by a negative number):
\(x\gt5\).

Step2: Solve the second inequality

Add \(10\) to both sides of \(4x - 10\lt -22\):
\(4x-10 + 10\lt -22+10\), so \(4x\lt - 12\).
Divide both sides by \(4\):
\(x\lt - 3\).

Answer:

The graph should have an open circle at \(x = 5\) with an arrow pointing to the right (for \(x\gt5\)) and an open circle at \(x=-3\) with an arrow pointing to the left (for \(x\lt - 3\)).