Question

answer is 6 , please give the solution . fast and correct . ​

Answer 1

Question

$\sf \dfrac{2x - 3}{6} - \dfrac{x - 5}{2} = \dfrac{x}{6}$

To find

value of x

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf \longmapsto \dfrac{2x - 3}{6} - \dfrac{x - 5}{2} = \dfrac{x}{6}$

=>LCM of 2 and 6 is 6

$\sf \longmapsto \dfrac{2x - 3 - 3(x - 5)}{6} = \dfrac{x}{6}$

$\sf \longmapsto \dfrac{2x - 3 - 3x + 15}{6} = \dfrac{x}{6}$

$\sf \longmapsto \dfrac{2x - 3x - 3 + 15}{6} = \dfrac{x}{6}$

$\sf \longmapsto \dfrac{ - x + 12}{6} = \dfrac{x}{6}$

Now cross multiply to both side =>

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You can also solve by this

$\sf =>-x+12=x$[Bases are same on both sides so ,it gets automatically cancelled]

$\sf =>12=2x$

$\sf=>x=6$

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$\sf \longmapsto6( - x + 12) = 6x$

$\sf \longmapsto - 6x + 72 = 6x$

$\sf \longmapsto72 = 12x$

$\sf \longmapsto \: x = \dfrac{72}{12} = 6$

$\sf \huge \bold{ x = 6}$

Check

$\sf \longmapsto \dfrac{2(6) - 3}{6} - \dfrac{6 - 5}{2} = \dfrac{6}{6} =1$

$\sf \longmapsto \dfrac{12 - 3}{6} - \dfrac{1}{2}$

$\sf \longmapsto \dfrac{9}{6} - \dfrac{1}{2} = \dfrac{9 - 3}{6} = \dfrac{6}{6} = 1$

Answer 2

Given :

$:\boxed{\bf\dfrac{2x-3}{6}-\dfrac{x-5}{2}=\dfrac{x}{6}}$

To Find :

The value of x.

Solution :

Analysis :

Here we have to solve the value of x by evaluating as per the signs.

Explanation :

$\\ :\implies\sf\dfrac{2x-3}{6}-\dfrac{x-5}{2}=\dfrac{x}{6}$

Taking LCM of 2 and 6 = 6,

Multiplying the quotient of the denominator with the numerator,

$\\ :\implies\sf\dfrac{2x-3-3(x-5)}{6}=\dfrac{x}{6}$

Expanding the brackets and changing the signs,

$\\ :\implies\sf\dfrac{2x-3-3x+15}{6}=\dfrac{x}{6}$

After evaluation,

$\\ :\implies\sf\dfrac{-x+12}{6}=\dfrac{x}{6}$

Cross Multiplying,

$\\ :\implies\sf6(-x+12)=6x$

Expanding the brackets,

$\\ :\implies\sf-6x+72=6x$

Transposing -6x to RHS,

$\\ :\implies\sf72=6x+6x$

After evaluation,

$\\ :\implies\sf72=12x$

$\\ :\implies\sf\dfrac{72}{12}=x$

$\\ :\implies\sf\cancel{\dfrac{72}{12}}=x$

$\\ :\implies\sf6=x$

$\\ :\implies\boxed{\bf x=6.}$

The value of x is 6.