Question

which graph represents the solutions to this inequality? 7m + 17 > -25 and -4m - 13 ≥ -33

Explanation:

Step1: Solve \(7m + 17 > -25\)

Subtract 17 from both sides: \(7m > -25 - 17\)
\(7m > -42\)
Divide by 7: \(m > -6\)

Step2: Solve \(-4m - 13 \geq -33\)

Add 13 to both sides: \(-4m \geq -33 + 13\)
\(-4m \geq -20\)
Divide by -4 (reverse inequality): \(m \leq 5\)

Step3: Find the intersection

The solution is \( -6 < m \leq 5 \). The graph should have an open circle at -6 (since \(m > -6\)) and a closed circle at 5 (since \(m \leq 5\)), with the line between them. This matches the first graph (top one) with open circle at -6, closed at 5, and line connecting.

Answer:

The top graph (with open circle at -6, closed at 5, and red line between)