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

Given:

Expression is $3 x-\frac{x-2}{3}=4-\frac{x-1}{4}$

To do:

We have to find the value of $x$.

Solution:

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

$\Rightarrow \frac {9x-x+2}{3}=\frac {16-x+1}{4}$

$\Rightarrow \frac {8x+2}{3}=\frac {17-x}{4}$

$\Rightarrow 4\times {8x+2}=3\times {17-x}$

$\Rightarrow 4\times {(8x+2)}=3\times {(17-x)}$               [by cross multiplication]

$\Rightarrow 32x+8=51-3x$      

$\Rightarrow 32x+3x=51-8$   

$\Rightarrow 35x=43$   

$\Rightarrow x=\frac {43}{35}$   

$\Rightarrow x=1.22$   

Thus, the value of $x$ is $1.22$.