Question

determine which graph represents the correct solution set to the inequality shown below
20 - 2p > -2(p + 2) + 4p

Explanation:

Step1: Expand the right - hand side

First, expand $-2(p + 2)+4p$ using the distributive property. $-2(p + 2)=-2p-4$, so $-2(p + 2)+4p=-2p-4 + 4p=2p-4$. The inequality becomes $20-2p>2p - 4$.

Step2: Move terms with $p$ to one side

Add $2p$ to both sides of the inequality: $20-2p+2p>2p-4 + 2p$, which simplifies to $20>4p-4$.

Step3: Isolate the term with $p$

Add 4 to both sides: $20 + 4>4p-4+4$, resulting in $24>4p$.

Step4: Solve for $p$

Divide both sides by 4: $\frac{24}{4}>\frac{4p}{4}$, so $6>p$ or $p < 6$.

Answer:

The correct graph is the one with an open - circle at 6 and an arrow pointing to the left. Among the options (not labeled here but based on the description of the graphs), it is the graph where the number line has an open circle at 6 and the line extends to the left towards negative infinity.