Question

How do you solve and graph `7-n<=19`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(7)` from each side of the inequality to isolate the `n` term while keeping the inequality balanced:

`7 - color(red)(7) - n <= 19 - color(red)(7)`

`0 - n <= 12`

`-n <= 12`

Now, multiply each side of the inequality by `color(blue)(-1)` to solve for `n` 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)(-1) xx -n color(red)(>=) color(blue)(-1) xx 12`

`n color(red)(>=) -12`

To graph this we will draw a vertical line at `-12` 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>=-12 [-20, 20, -10, 10]}