Question

what is the correct graph that represents the answer for the following inequality?

2c + 4 ≤ 14

Explanation:

Step1: Solve the inequality

Subtract 4 from both sides of \(2c + 4\leq14\):
\(2c+4 - 4\leq14 - 4\), which simplifies to \(2c\leq10\).

Step2: Isolate the variable

Divide both sides by 2: \(\frac{2c}{2}\leq\frac{10}{2}\), so \(c\leq5\).

Step3: Analyze the graph representation

When \(c\leq5\), on the number - line, we have a closed circle at 5 (because the inequality includes equality, \(\leq\)) and the arrow points to the left (towards smaller values).

Answer:

The third graph (with a closed circle at 5 and the arrow pointing to the left) is the correct representation.