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, we get $p < - 3$.

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, we get $p>23$.

Step3: Analyze the graph

The solution of the compound - inequality $-4p + 27>39$ or $3p - 10>59$ is $p < - 3$ or $p>23$. The graph with open - circles at $p=-3$ and $p = 23$ and arrows pointing in the directions of values less than - 3 and greater than 23 represents the solution.

Answer:

The graph with open - circles at $-3$ and $23$ and arrows pointing away from each other (one to the left of $-3$ and one to the right of $23$) represents the solution.