Solve for $x$:$ \frac{3 x-2}{3}+\frac{2 x+3}{2}=x+\frac{7}{6} $

Given: 

Expression: $\frac{3 x-2}{3}+\frac{2 x+3}{2}=x+\frac{7}{6}$

To do: 

To solve the expression $\frac{3 x-2}{3}+\frac{2 x+3}{2}=x+\frac{7}{6}$

Solution:

$\frac{3 x-2}{3}+\frac{2 x+3}{2}=x+\frac{7}{6}$

$\Rightarrow\frac{2(3x-2)+3(2x+3)}{6}=\frac{6x+7}{6}$       $\left[taking\ L.C.M\right]$

$\Rightarrow\frac{6x-4+6x+9}{6}=\frac{6x+7}{6}$

$\Rightarrow\frac{12x+5}{6}=\frac{6x+7}{6}$

$\Rightarrow 6\left(12x+5\right)=6\left(6x+7\right)$   $\left[by\ cross\ multiplication\right]$

$\Rightarrow 72x+30=36x+42$

$\Rightarrow 72x-36x=42-30$

$\Rightarrow 36x=12$

$\Rightarrow x=\frac{12}{36}$

$\Rightarrow x=\frac{1}{3}$

Thus, the value of $x=\frac{1}{3}$.

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Updated on: 10-Oct-2022

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