[quote="esledge"]
So for this question: Is sqrt[(x-3)^2] = 3-x?
Rephrase to: Is |x-3| = 3-x?
If stuff in the absolute value sign is positive or zero, this becomes:
Is x-3 = 3-x?
Is 2x = 6?
Is x = 3?
If stuff in the absolute value sign is negative, this becomes:
Is -(x-3) = 3-x?
Is -x+3 = 3-x?
The answer is yes for all x, but remember this was just "all x" such that x-3 was negative, or x < 3: So we ask "Is x < 3?"
Can you please explain me how did you get to the conclusion that x<3. When I consider -
Is -(x-3) = 3-x? I get the answer as x=0. Then if i substitute these back in the equation we still get both of them as possible solutions. Why didn't you think that this equation has two solutions x=0, x=3. I wanted to understand the thought process behind getting to x<3