Find the value of $x$ if:
$\frac{2x\ +\ 7}{5} \ -\ \frac{3x\ +\ 11}{2} \ =\ \frac{2x\ +\ 8}{3} \ -\ 5$

Given: $\frac{2x\ +\ 7}{5} \ -\ \frac{3x\ +\ 11}{2} \ =\ \frac{2x\ +\ 8}{3} \ -\ 5$

To find: Here we have to find the value of $x$ if $\frac{2x\ +\ 7}{5} \ -\ \frac{3x\ +\ 11}{2} \ =\ \frac{2x\ +\ 8}{3} \ -\ 5$.

Solution:

$ \begin{array}{l}
\frac{2x\ +\ 7}{5} \ -\ \frac{3x\ +\ 11}{2} \ =\ \frac{2x\ +\ 8}{3} \ -\ 5\\
\\
\\
\\
\frac{2( 2x\ +\ 7) \ -\ 5( 3x\ +\ 11)}{10} \ =\ \frac{( 2x\ +\ 8) \ -\ 3( 5)}{3}\\
\\
\\
\\
\frac{4x\ +\ 14\ -\ 15x\ -\ 55}{10} \ =\ \frac{2x\ +\ 8\ -\ 15}{3}\\
\\
\\
\\
\frac{-\ 11x\ -\ 41}{10} \ =\ \frac{2x\ -\ 7}{3}\\
\\
\\
\\
3( -\ 11x\ -\ 41) \ =\ 10( 2x\ -\ 7)\\
\\
\\
\\
-\ 33x\ -\ 123\ =\ 20x\ -\ 70\\
\\
\\
\\
-\ 33x\ -\ 20x\ =\ -\ 70\ +\ 123\\
\\
\\
-\ 53x\ =\ 53\\
\\
\\
x\ =\ -\ \frac{53}{53}\\
\\
\\
\mathbf{x\ =\ -\ 1}
\end{array}$

So, the value of $x$ is -1.

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Updated on: 10-Oct-2022

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