Should we use or or and when rewriting the inequality?
Inequality: |n-3|>9 Solution: n<- 6 or n>12
Practice makes perfect
In order to rewrite this sentence into an absolute value inequality, we should first remember the standard form for an absolute value equation.
|x-Midpoint|=Distance
Let n be our variable. We can fill in the numerical information.
& A number... 9units from3
& | n- 3|... 9Since we need the distance from 3 to be more than 9 units, we will use >.
& A numberis more than 9units from3
& | n- 3|> 9
Now we can solve this inequality by splitting the absolute value into two cases. Because we want the distance to be greater than 9, we will need to write an or inequality.
First case: &n-3>9
Second case: &n-3<- 9
We can solve these cases separately and then combine the results. We will begin with the first case.
