rrsnathan wrote:

ratinarace wrote:

the equation has 3 intervals 2, 3 , and 5. i.e 4 segments x<2, 2<x<3, 3<x<5, 5<x.

1) When X>5 none of the brackets will change the sign and hence

(x-2)-(x-3) = (x-5)-------> x=6 ..We accept this solution as it satisfies the equation.

Now since we know x=6 is one of the solution we know the answer could be C or D

2) When 3<x<5 here (x-5) will change the sign

(x-2)-(x-3) = -(x-5) ------>x=4 ..We accept the solution as 3<4<5

We can stop solving here as the only set consisting both 6 and 4 is set C hence correct answer is C

Hi,

I have a doubt on this

How can we say X>5 none of the brackets will change the sign and When 3<x<5 here (x-5) will change the sign?

Wat is it to define this?

Please help me in this

Thanks in advance.

Hi rrsnathan,

The eqn :

|x-2|-|x-3|=|x-5|

is about modulus function.

The modulus always takes the magnitude i.e.

|2| = 2 and also |-2| = 2,

so you can see that for negative expression y ; |y | = - (y)

which is same as changing the sign , to make it positive

So,when x>5, all the modulus expression

|x-2|,|x-3|and |x-5| are positive,so we need not change sign

when 3<x<5,

|x-2| is positive , |x-3| is positive and |x-5| is negative,

so we need to change the sign for |x-5| i.e.

|x-5| = - (x-5)That's why the equation

|x-2|-|x-3|=|x-5|becomes

(x-2) -(x-3) = - (x-5) this is what Ratinarace meant, although explained confusinglyHope above example clears your doubt

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