I suppose you could always graph the function, see where it crosses the line ...
The question:
Solve for x,
|2x-1|+|x+3| = 5
What's the best way to attempt questions involving the addition of absolute values? I can consider the case when x is negative, and x is positive, but that seems like an elementary approach. Is there a better way?
Note: I'm not interested in the solution, I'm interested in the method. Thanks.
Why would considering the two cases where x is negative and positive be an elementary approach? Also, even if it is, what's wrong with an elementary approach? By doing this, we get x = 1 and -1. I don't see anything wrong with that. As Prove It has already said, you could graph it, but that seems like more work than is necessary.
Similarly, you could say
Both and are gives
and for that case you must have and so
Next, and
This is not possible as we cannot have and
However, we can have and
In this case you have
(You must verify that the solution given falls correctly within the required range)
Finally, if and are both
you find that requires x to be above
which causes a contradiction.
So two of the 4 options are valid.