do we write an absolute value inequalitiy to fit .....

[Guest]

We have a graph showing that it is all numbers equal to 5 and 10 and all between 5 & 10...but how do we write an absolute value inequalitiy to fit this graph?? :?

 

[soroban]

Hello, 4 little piggies mom!

We have a graph showing that it is all numbers equal to 5 and 10 and all between 5 & 10.
but how do we write an absolute value inequalitiy to fit this graph?

Remember my reference to "distance"?

\(\displaystyle \;\;\;\,-\,-\,\bullet========\bullet\,-\,-\)
\(\displaystyle \;\;\;\;\;\;\:\:5\;\;\;\;\;\;\uparrow\;\;\;\;\;\;\,10\)
\(\displaystyle \;\;\;\;\;\;\;\;\;\;\;\;\;\:7.5\)

Can you see that we can use: \(\displaystyle \;|x\,-\,7.5|\:\leq\:2.5\)