Question

How do you solve `(1/3)^x-9<18` using a graph?

Answer 1

See below.

Explanation:

`(1/3)-9<18color(white)(8888)` , `(1/3)-27<0`

First Graph `y=(1/3)-27`.

This will give you the boundary between the included and excluded regions. Remember to use a dashed line, as this is a less than and not a less than or equal to inequality, so the line will not be an included region.

With the equation plotted, you will have to possible regions. These have been marked A and B on the graph. We need to test a pair of coordinates in each region to see which region satisfies the inequality.

Region A

coordinates `(5,10)`

`(1/3)^(5)-27<10`

`243-27<10`

`1/243-27<10color(white)(8888)` TRUE

A is an included region.

Now we have found our region, we do not really need to test B. Will will check this just for clarity.

Region B

coordinates `(5,-40)`

`(1/3)^(5)-27<-40`

`1/243-27<-40color(white)(8888)`FALSE

B is an excluded region.

Shade region A