Question

solve the inequality and graph the solution.
-3 > 8(p + 1) + 5
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Expand the right - hand side

First, expand \(8(p + 1)+5\) using the distributive property \(a(b + c)=ab+ac\). So \(8(p + 1)+5=8p+8 + 5=8p + 13\). The inequality becomes \(-3>8p + 13\).

Step2: Isolate the variable term

Subtract 13 from both sides of the inequality. \(-3-13>8p+13 - 13\), which simplifies to \(-16>8p\).

Step3: Solve for \(p\)

Divide both sides of the inequality by 8. \(\frac{-16}{8}>\frac{8p}{8}\), so \(p<-2\).

Answer:

The solution of the inequality is \(p < - 2\). On the number - line, we have an open circle at \(-2\) (because the inequality is strict, \(p\) cannot equal \(-2\)) and the line extends to the left of \(-2\).