Question

which graph represents the solutions to this inequality? -4p + 27 > 39 or 3p - 10 > 59

Explanation:

Step1: Solve the first inequality

Solve \(-4p + 27>39\).
Subtract \(27\) from both sides: \(-4p>39 - 27\), so \(-4p>12\).
Divide both sides by \(-4\) (and reverse the inequality sign): \(p<-3\).

Step2: Solve the second inequality

Solve \(3p - 10>59\).
Add \(10\) to both sides: \(3p>59 + 10\), so \(3p>69\).
Divide both sides by \(3\): \(p>23\).

Answer:

The solution of the compound inequality \( - 4p + 27>39\) or \(3p - 10>59\) is \(p<-3\) or \(p>23\). So the graph with an open circle at \(-3\) (shading to the left) and an open circle at \(23\) (shading to the right) is the correct one.