# How do you solve and graph 2p + 5 ≥ 3p - 10 ?

May 8, 2017

See a solution process below:

#### Explanation:

Step 1) Subtract $\textcolor{red}{2 p}$ and add $\textcolor{b l u e}{10}$ to each side of the inequality to solve for $p$ while keeping the inequality balanced:

$- \textcolor{red}{2 p} + 2 p + 5 + \textcolor{b l u e}{10} \ge - \textcolor{red}{2 p} + 3 p - 10 + \textcolor{b l u e}{10}$

$0 + 15 \ge \left(- \textcolor{red}{2} + 3\right) p - 0$

$15 \ge 1 p$

$15 \ge p$

Step 2) To state the solution in terms of $p$ we can reverse or "flip" the entire inequality:

$p \le 15$