Posted by Shreya on Wednesday, January 18, 2012 at 10:09pm.
if 2x-3 >= 0 then you have
2x-3 - |2x-5| = 0
Now, if 2x-5 >= 0, that gives
2x-3 - (2x-5) = 0
2 = 0
no good
If 2x-5 < 0 you have
2x-3 - -(2x-5) = 0
2x-3 + 2x-5 = 0
4x - 8 = 0
x = 2
since x=2 satisfies both conditions
2x-56 < 0 and 2x-3 >= 0, it's a solution.
Work through the other possibilities to find that x=2 is the only solution.
Makes sense, since the graphs of the two absolute values are v-shaped with equal slopes, so they intersect in only one point.
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