Solve: $ \frac{1}{2}-\frac{9-x}{11}=\frac{3 x}{12} $.

Given:

Given equation is $\frac{1}{2}-\frac{9-x}{11}=\frac{3x}{12}$.

To do:

We have to solve the given equation.

Solution:

$ \begin{array}{l}
\frac{1}{2} -\frac{9-x}{11} =\frac{3x}{12}\\
\\
\frac{1}{2} =\frac{9-x}{11} +\frac{3x}{12}\\
\\
\frac{1}{2} =\frac{12( 9-x) +11( 3x)}{132} \ \ \ \ [ LCM\ of\ 11\ and\ 12\ is\ 132]\\
\\
\frac{1}{2} =\frac{12( 9) -12( x) +33x}{132}\\
\\
\frac{1}{2} =\frac{108-12x+33x}{132}\\
\\
\frac{1}{2} =\frac{21x+108}{132}\\
\\
132\times 1=2( 21x+108)\\
\\
132=2( 21x) +2( 108)\\
\\
132=42x+216\\
\\
42x=132-216\\
\\
42x=-84\\
\\
x=\frac{-84}{42}\\
\\
x=-2
\end{array}$

The value of x is $-2$.  

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Updated on: 10-Oct-2022

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