Question

Solve for $x$:

$\frac{7x-1}{4}-\frac{1}{3}(2x-\frac{1-x}{2})=\frac{19}{3}$

Answer 1

$\frac{7x-1}{4}-\frac{1}{3}(2x-\frac{1-x}{2})=\frac{19}{3}$

$\Rightarrow \frac{7x-1}{4}-\frac{2x}{3}+\frac{1-x}{6}=\frac{19}{3}$

taking LCM

$\Rightarrow \frac{3(7x-1)-4\left(2x\right)+2(1-x)}{12}=\frac{19}{3}$

$\Rightarrow 21x-3-8x+2-2x=19\times 4$

$\Rightarrow 21x-10x=76+1$

$11x=77$

x=7

$\therefore$ value of x is 7.