Question

which graph represents the solutions to this inequality? -3q + 11 ≥ 38 or -2q + 39 < 45

Explanation:

Step1: Solve the first inequality

Solve \(-3q + 11\geq38\).
Subtract \(11\) from both sides: \(-3q\geq38 - 11\), so \(-3q\geq27\).
Divide both sides by \(-3\) (and reverse the inequality sign): \(q\leq - 9\).

Step2: Solve the second inequality

Solve \(-2q+39 < 45\).
Subtract \(39\) from both sides: \(-2q<45 - 39\), so \(-2q < 6\).
Divide both sides by \(-2\) (and reverse the inequality sign): \(q>-3\).

Answer:

The graph with a closed circle at \(-9\) (since \(q\leq - 9\)) and an open circle at \(-3\) (since \(q > - 3\)) represents the solutions.