Question

# Solve for $$x$$: $$\displaystyle \frac{3x}{4}-\frac{(x-1)}{3}=\frac{(x-2)}{2}$$.

A
9
B
14
C
16
D
11

Solution

## The correct option is C $$16$$Given, $$\displaystyle \frac{3x}{4}-\frac{(x-1)}{3}=\frac{(x-2)}{2}$$L.C.M. of denominator $$=12$$$$\therefore$$ Multiplying each term by $$12$$, we get $$\displaystyle 12\times \frac{3x}{4}-12\times \frac{(x-1)}{3}=12\times \frac{(x-2)}{2}$$$$\Rightarrow 9x-4(x-1)=6(x-2)$$$$\Rightarrow 9x-4x+4=6x-12$$$$\Rightarrow 5x+4=6x-12$$$$\Rightarrow x=16$$Hence, required value of $$x$$ is $$16$$.Mathematics

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