If |x-2|+|x-3|=7, then x=

Here x = 2 and 3 are the critical points.when x<2, |x-2|=-(x-2), |x-3|=-(x-3)∴ x=-1 is a solution.When 2≤x<3, |x-2|=x-2, |x-3|=-(x-3)∴The equation reduces to x-2+3-x=7⇒1=7∴ No solution in this case.When x≥3, the equation reduces tox-2+x-3=7⇒x=6>3Hence we get, x=6 or -1