Question

How do you solve and graph `-23>=q-30`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(30)` to each side of the inequality to solve for `q` while keeping the inequality balanced:

`-23 + color(red)(30) >= q - 30 + color(red)(30)`

`7 >= q - 0`

`7 >= q`

To state the solution in terms of `q` we can reverse or "flip" the entire inequality:

`q <= 7`

To graph this we will draw a vertical line at `7` 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 left side of the line because the inequality operator also contains a "less than" clause:

graph{x<= 7 [-10, 20, -7.50, 7.50]}