Question

How do you solve and graph `-p/7> -9`?

Answer 1

See a solution process below:

Explanation:

First, multiply each side of the inequality by `color(blue)(-7)` 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:

`color(blue)(-7) xx p/(-7) color(red)(<) color(blue)(-7) xx -9`

`cancel(color(blue)(-7)) xx p/color(blue)(cancel(color(black)(-7))) color(red)(<) 63`

`p < 63`

To graph this we will draw a vertical line at `63` on the horizontal axis.

The line will be a dashed line because the inequality operator does not contain an "or equal to" clause.

We will shade to the left side of the line because the inequality operator does contains a "less than" clause:

graph{x<63 [-100, 100, -50, 50]}