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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 $1.22$.
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