$$\left. \begin{array} { l } { \frac { 7 x - 1 } { 4 } - \frac { 1 } { 3 } ( 2 x - \frac { 1 - x } { 2 } ) = \frac { 19 } { 3 } } \end{array} \right.$$
$x=7$
$$3\left(7x-1\right)-4\left(2x-\frac{1-x}{2}\right)=76$$
$$21x-3-4\left(2x-\frac{1-x}{2}\right)=76$$
$$21x-3-4\left(2x-\left(\frac{1}{2}-\frac{1}{2}x\right)\right)=76$$
$$21x-3-4\left(2x-\frac{1}{2}-\left(-\frac{1}{2}x\right)\right)=76$$
$$21x-3-4\left(2x-\frac{1}{2}+\frac{1}{2}x\right)=76$$
$$21x-3-4\left(\frac{5}{2}x-\frac{1}{2}\right)=76$$
$$21x-3-4\times \frac{5}{2}x-4\left(-\frac{1}{2}\right)=76$$
$$21x-3+\frac{-4\times 5}{2}x-4\left(-\frac{1}{2}\right)=76$$
$$21x-3+\frac{-20}{2}x-4\left(-\frac{1}{2}\right)=76$$
$$21x-3-10x-4\left(-\frac{1}{2}\right)=76$$
$$21x-3-10x+\frac{-4\left(-1\right)}{2}=76$$
$$21x-3-10x+\frac{4}{2}=76$$
$$21x-3-10x+2=76$$
$$11x-3+2=76$$
$$11x-1=76$$
$$11x=76+1$$
$$11x=77$$
$$x=\frac{77}{11}$$
$$x=7$$
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