Question

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

• A. $9$
• B. $14$
• C. $16$
• D. $11$

Answer 1

The correct option is C $16$

Given, $\frac{3x}{4}-\frac{(x-1)}{3}=\frac{(x-2)}{2}$
L.C.M. of denominator $=12$
$\therefore$ Multiplying each term by $12$, we get
$12\times \frac{3x}{4}-12\times \frac{(x-1)}{3}=12\times \frac{(x-2)}{2}$
$\Rightarrow 9x-4(x-1)=6(x-2)$
$\Rightarrow 9x-4x+4=6x-12$
$\Rightarrow 5x+4=6x-12$

$\Rightarrow x=16$
Hence, required value of $x$ is $16$.