Question

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

Explanation:

Step1: Solve the first inequality

Solve \(7m + 17> - 25\).
Subtract \(17\) from both sides: \(7m>-25 - 17\), so \(7m>-42\).
Divide both sides by \(7\): \(m > - 6\).

Step2: Solve the second inequality

Solve \(-4m-13\geq - 33\).
Add \(13\) to both sides: \(-4m\geq-33 + 13\), so \(-4m\geq-20\).
Divide both sides by \(-4\) (and reverse the inequality sign): \(m\leq5\).

Answer:

The solution of the compound - inequality \(7m + 17> - 25\) and \(-4m-13\geq - 33\) is \(-6 < m\leq5\). So the graph with an open circle at \(-6\) and a closed circle at \(5\) (the middle - one among the three given graphs) represents the solutions.