# How do you solve and graph -15p ≤ -90 ?

Oct 3, 2017

See a solution process below:

#### Explanation:

First, divide each side of the inequality by $\textcolor{b l u e}{- 15}$ to solve for $p$ while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

$\frac{- 15 p}{\textcolor{b l u e}{- 15}} \textcolor{red}{\ge} \frac{- 90}{\textcolor{b l u e}{- 15}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{- 15}}} p}{\cancel{\textcolor{b l u e}{- 15}}} \textcolor{red}{\ge} 6$

$p \textcolor{red}{\ge} 6$

To graph this we will draw a vertical line at $6$ on the horizontal axis.

The line will be a solid line because the inequality operator contains an "or equal to" clause.

We will shade to the right side of the line because the inequality operator also contains a "greater than" clause:

graph{x>=6 [-15, 15, -7.50, 7.50]}