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1.3   Check by Graphing

Example 1.     Solve  .

If we type in our graphing calculator:   and  ,  we get a graph like the following :   (Your resolution will probably be different.)

We notice that the graphs intersect at two different points:  one when  and the other when .

Example 2.     

The numbers between -3 and 13 are less than 8 units away from 5.

We can also use the graph from Example 1 above to verify our answers.  Note that all the inputs between -3 and 13 have outputs that are below the line representing .

Example 3   

The numbers that are less than -3 and greater than 13 are more than 8 units away from 5.

We can again use the graph from Example 1 above to verify our answers.  Note that all the inputs that are less than -3 and greater than 13 have outputs that are above the line representing .

Example 4.    

If we type in our graphing calculator:   and  ,  we get a graph like the following :

We notice that the graphs intersect at two different points:  one when  and the other when .

Just for fun, we might try getting one side = 0 and plotting it, like so:  

How does this graph confirm our solution as well?

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