Posted by T.Gracken on October 20, 2002 at 09:35:53:
In Reply to: simple absolute values posted by dave on October 19, 2002 at 19:51:07:
: for the life of me I cannot remember how to solve:
: could someone please explain the process for soving these types of absolute value equations...
I wouldn't necessarily call this simple, but...
you could start by isolating one of the absolute values
|2x-1|= 3 + |x+5|
Then we have
2x-1 = 3 + |x+5|, or 2x-1 = -3 - |x+5|
Case 1: 2x-1 = 3 + |x+5|
=> 2x-4 = |x+5|
=> x+5=2x-4, or x+5=-2x+4
=> x=9, or x=-1/3
upon checking, x=-1/3 is extraneous.
Case 2: 2x-1 = -3 - |x+5|
I'll let you do this one. (and don't forget to check the results for extraneous roots).
You have at least one solution now, x=9.
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