Question

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

Answer 1

See a solution process below:

Explanation:

First, divide each side of the inequality by `color(blue)(-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:

`(-15p)/color(blue)(-15) color(red)(>=) (-90)/color(blue)(-15)`

`(color(blue)(cancel(color(black)(-15)))p)/cancel(color(blue)(-15)) color(red)(>=) 6`

`p color(red)(>=) 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]}