Question

which graph represents the solutions to this inequality? 4c + 8 ≤ -36 or -5c + 15 < 25

Explanation:

Step1: Solve the first inequality

Solve \(4c + 8\leq - 36\). Subtract 8 from both sides: \(4c\leq-36 - 8\), so \(4c\leq-44\). Divide both sides by 4, we get \(c\leq - 11\).

Step2: Solve the second inequality

Solve \(-5c + 15\lt25\). Subtract 15 from both sides: \(-5c\lt25 - 15\), so \(-5c\lt10\). Divide both sides by - 5 and reverse the inequality sign, we get \(c\gt - 2\).

Step3: Analyze the "or" condition

The solution of the compound - inequality \(4c + 8\leq - 36\) or \(-5c + 15\lt25\) is \(c\leq - 11\) or \(c\gt - 2\).
The graph will have a closed - circle at \(c=-11\) (because of \(\leq\)) with an arrow pointing to the left and an open - circle at \(c = - 2\) (because of \(\lt\)) with an arrow pointing to the right.

Answer:

The graph with a closed - circle at \(-11\) and an arrow pointing left and an open - circle at \(-2\) and an arrow pointing right.