## Question

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

## Answers

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

AandBon the graph. We need to test a pair of coordinates in each region to see which region satisfies the inequality.

Region Acoordinates

#(5,10)#

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

#243-27<10#

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

Ais 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 Bcoordinates

#(5,-40)#

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

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

Bis an excluded region.Shade region

A