Graphing absolute values (1 Viewer)

[Nathan Truong]

Evening all.

The question is:

Solve l2x+2l + l3x-6l = 5

Thank you.

 

[twinklegal19]

One approach is to graph y=|2x+2| and y=|3x-6| separately on the same axis. Add the ordinates to draw the new curve and see where it cuts the line y=5.

 

[Deliriously]

Another method, which i prefer, is rearrange the equation to: |2x+2|= 5-|3x-6|
then graph y=|2x+2| and y= 5-|3x-6|
which yields you:
http://www.wolframalpha.com/input/?i=|2x+2|=5-|3x-6|
and you can clearly see from the graph there are no solutions.

Else, if the graphs were to intersect, you would find the P.O.I by solving it normally.

 

[deswa1]

Or finally, a third method if you are solid and quick at algebra but not so good on the graphing (like me) is consider cases of x. Like consider where x>2, then the equation becomes 5x=9 which has no solution in the domain etc. Though graphing is generally easier- just throwing this method out there is case you wanted to consider it

 

[braintic]

OR:
Rewrite 2|x+1| + 3|x-2| = 5
ie. "Find values of x such that twice the distance of x from -1 plus three times the distance of x from 2 is equal to 5.

If you are clever enough, you can come up with the answer by considering these distances.