Q. 1 A3.7( 3 Votes )

<span lang="EN-US

Answer :

.|x – 1| = |x – 3|

This can be solved in the following cases:


Case1 : when x>1, |x -1| = x -1 and x>3, |x-3| = x-3


x-1 = x-3 no solution as x gets cancelled out on both sides……….eq(1)


Case2 : when x>1, |x-1| = x -1 and x<3, |x-3| = -(x-3)


x-1 = -(x-3)


x-1 = 3-x


2x = 3 + 1


2x = 4


x = 2………………..eq(2)


Case3 : when x<1, |x-1| = -(x-1) and x>3, |x-3| = x-3


-(x-1) = (x-3)


-x + 1 = x-3


-2x = -3-1 = -4


2x = 4


x = 2………………..eq(3)


Case4 : when x<1, |x-1| = -(x-1) and x<3, |x-3| = -(x-3)


-(x-1) = -(x-3)


-x + 1 = -x + 3 no solution as x gets cancelled out on both sides…………………..eq(4)


Now from eq(2) ans eq(3), we have x = 2 as the solution of the equation.


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