SOLUTION: Solve for real values of x. absolutevalue(x-3) = 3-x I know to set the absolute value up to equal a positive and negative possiblity and so that makes x-3 = 3-x and x-3 = -

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Question 204633: Solve for real values of x.
absolutevalue(x-3) = 3-x
I know to set the absolute value up to equal a positive and negative possiblity and so that makes
x-3 = 3-x and x-3 = -3+x
For the first I got x = 3 but the second I got 0 = 0 and that's where I am confused. Did I do something wrong?
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
You have the right answers. What this means is that the right side 3-x is the EXACT same as the negative half of the absolute value (go ahead and graph to confirm). So this means that if you plug in any number less than or equal 3, you'll get 0=0. So this means that the solution set is the set of all x values less than or equal 3.


Answer by Edwin McCravy(20086)   (Show Source): You can put this solution on YOUR website!



Let's use the principle , to replace
the left side:







Now we use the principle that  if and only if 

Therefore 

is true  if and only if  



Subtract 3 from both sides:



Multiply through by -1, which reverses the inequality:



Or in interval notation 

The equation has infinitely many solutions.

Edwin
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