answer is 6 , please give the solution . fast and correct .
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answer is 6 , please give the solution . fast and correct .
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Question
[tex] \sf \dfrac{2x - 3}{6} - \dfrac{x - 5}{2} = \dfrac{x}{6} [/tex]
To find
value of x
[tex]\sf\huge\bold{\underline{\underline{{Solution}}}}[/tex]
[tex]\sf \longmapsto \dfrac{2x - 3}{6} - \dfrac{x - 5}{2} = \dfrac{x}{6} [/tex]
=>LCM of 2 and 6 is 6
[tex]\sf \longmapsto \dfrac{2x - 3 - 3(x - 5)}{6} = \dfrac{x}{6} [/tex]
[tex]\sf \longmapsto \dfrac{2x - 3 - 3x + 15}{6} = \dfrac{x}{6} [/tex]
[tex]\sf \longmapsto \dfrac{2x - 3x - 3 + 15}{6} = \dfrac{x}{6} [/tex]
[tex]\sf \longmapsto \dfrac{ - x + 12}{6} = \dfrac{x}{6} [/tex]
Now cross multiply to both side =>
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You can also solve by this
[tex]\sf =>-x+12=x[/tex][Bases are same on both sides so ,it gets automatically cancelled]
[tex]\sf =>12=2x[/tex]
[tex]\sf=>x=6[/tex]
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[tex]\sf \longmapsto6( - x + 12) = 6x[/tex]
[tex]\sf \longmapsto - 6x + 72 = 6x[/tex]
[tex]\sf \longmapsto72 = 12x[/tex]
[tex]\sf \longmapsto \: x = \dfrac{72}{12} = 6[/tex]
[tex] \sf \huge \bold{ x = 6}[/tex]
Check
[tex]\sf \longmapsto \dfrac{2(6) - 3}{6} - \dfrac{6 - 5}{2} = \dfrac{6}{6} =1[/tex]
[tex]\sf \longmapsto \dfrac{12 - 3}{6} - \dfrac{1}{2}[/tex]
[tex]\sf \longmapsto \dfrac{9}{6} - \dfrac{1}{2} = \dfrac{9 - 3}{6} = \dfrac{6}{6} = 1[/tex]
Verified answer
Given :
[tex]:\boxed{\bf\dfrac{2x-3}{6}-\dfrac{x-5}{2}=\dfrac{x}{6}}[/tex]
To Find :
The value of x.
Solution :
Analysis :
Here we have to solve the value of x by evaluating as per the signs.
Explanation :
[tex]\\ :\implies\sf\dfrac{2x-3}{6}-\dfrac{x-5}{2}=\dfrac{x}{6}[/tex]
Taking LCM of 2 and 6 = 6,
Multiplying the quotient of the denominator with the numerator,
[tex]\\ :\implies\sf\dfrac{2x-3-3(x-5)}{6}=\dfrac{x}{6}[/tex]
Expanding the brackets and changing the signs,
[tex]\\ :\implies\sf\dfrac{2x-3-3x+15}{6}=\dfrac{x}{6}[/tex]
After evaluation,
[tex]\\ :\implies\sf\dfrac{-x+12}{6}=\dfrac{x}{6}[/tex]
Cross Multiplying,
[tex]\\ :\implies\sf6(-x+12)=6x[/tex]
Expanding the brackets,
[tex]\\ :\implies\sf-6x+72=6x[/tex]
Transposing -6x to RHS,
[tex]\\ :\implies\sf72=6x+6x[/tex]
After evaluation,
[tex]\\ :\implies\sf72=12x[/tex]
[tex]\\ :\implies\sf\dfrac{72}{12}=x[/tex]
[tex]\\ :\implies\sf\cancel{\dfrac{72}{12}}=x[/tex]
[tex]\\ :\implies\sf6=x[/tex]
[tex]\\ :\implies\boxed{\bf x=6.}[/tex]
The value of x is 6.