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If  $\mid 4X-7 \mid =5$ then the values of $2\mid X\mid -\mid -X\mid$ is:

1. $\quad 2,\left(\dfrac{1}{3}\right)$
2. $\left(\dfrac{1}{2}\right),3$
3. $\left(\dfrac{3}{2}\right),9$
4. $\left(\dfrac{2}{3}\right),9$

### 1 comment

We are getting x=1/2,3.both are positive

|X|= X, when X>0

=- X when X<0

Similarly ,|-X| =-X when X <0

=-(-X) when X>0

2|X|-|X|=2X-(-(-X))=2X-X=X

$\mid 4X-7\mid = 5$  ,since it is in absolute form the regular form of this equation is given as

$(4X-7)= 5$

$(4X-7)=-5$

By solving the above equations we get the following answer

$X=\frac{1}{2}, X = 3$

Now $2\mid X\mid -\mid -X\mid = 2\mid X \mid - \mid X| = \mid X \mid$.

So, our answer will be $B.$
by

Its not specific for x = 1/2 or 3. In general when you evaluate

f(Y) = 2|X| - |-X|

= 2 |X| - |X|

= |X|

It is a corner case but it is asking for absolute value of X here.

4x-7= 5     if 4x-7 >0   here we get x=3

4x-7= -5     if 4x-7 <=0 here we get x =0.5

= 2 |X| - |X|

= |X|  then           3          if x>0

0.5      if x<=0      so B is anwser   @arjun , @arjun plz verify it

Here why are giving "values" shouldn't it be ((3/2) when x=1/2   & (9) when x=3 