|x-3|=|3-x| find x???
Sorry, I only give jocose help.
Since 3-x = -(x-3)
|x-3| = |3-x| for all values of x
square both = > we will have (x-3)^2 = ( 3-x)^2
To find the value(s) of x in the equation |x-3|=|3-x|, we need to consider two cases:
Case 1: (x-3) = (3-x)
- In this case, the absolute value signs cancel out.
- Simplifying the equation, we have x - 3 = 3 - x.
- Combining like terms, we get 2x = 6.
- Dividing both sides by 2, we find x = 3.
Case 2: (x-3) = -(3-x)
- In this case, the right side of the equation is negated because of the negative sign.
- Expanding the equation, we have x - 3 = -3 + x.
- Rearranging the terms, we obtain x - x = -3 + 3.
- Simplifying the equation, we see that 0 = 0.
- Since 0 = 0 is always true, it means that for any value of x, the equation is satisfied.
Thus, the equation |x-3|=|3-x| has two solutions: x = 3 and x can be any real number.