| Statement 1: \[X=\frac{1}{2}\] is the solution of \[\frac{(2x-3)}{4}-\frac{(2x-1)}{2}=\frac{x-2}{3}\]. |
| Statement 2: \[x=\frac{63}{2}\] is the solution of \[\frac{2x-17}{2}-\left( x-\frac{x-1}{3} \right)=12\]. |
A) Only Statement-1
B) Only Statement-2
C) Both Statement -1 and Statement - 2
D) Neither Statement -1 nor Statement - 2
Correct Answer: A
Solution :
Statement-1: \[\frac{(2x-3)}{4}-\frac{(2x-1)}{2}=\frac{x-2}{3}\] \[\Rightarrow \frac{2x-3-4x+2}{4}=\frac{x-2}{3}\] \[\Rightarrow \frac{-2x-1}{4}=\frac{x-2}{3}\Rightarrow -6x-3=4x-8\] \[\Rightarrow -6x-4x=-8+3\] \[\Rightarrow -10x=-5\Rightarrow x=\frac{1}{2}\] So, Statement-1 is true. Statement - 2:\[\frac{2x-17}{2}-\left( x-\frac{x-1}{3} \right)=12\] \[\Rightarrow \frac{2x-17}{2}-\left( \frac{3x-x+1}{3} \right)=12\] \[\Rightarrow \frac{3(2x-17)-2(2x+1)}{6}=12\] \[\Rightarrow 6x-51-4x-2=12\times 6\] \[\Rightarrow 2x-53=72\Rightarrow 2x=72+53\] \[\Rightarrow x=\frac{125}{2}\] So, Statement-2 is false.
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