Find the value of $x$:$\frac{7}{2} x-\frac{5}{2} x=\frac{20 x}{3}+10$.
Given: Expression: $\frac{7}{2} x-\frac{5}{2} x=\frac{20 x}{3}+10$.
To do: To find the value of $x$.
Solution:
$\frac{7}{2} x-\frac{5}{2} x=\frac{20 x}{3}+10$
$\Rightarrow \frac{7}{2} x-\frac{5}{2} x-\frac{20 x}{3}+10$
$\Rightarrow \frac{7x-5x-20x}{2}=10$
$\Rightarrow \frac{7x-25x}{2}=10$
$\Rightarrow \frac{-18x}{2}=10$
$\Rightarrow -18x==10\times 2$
$\Rightarrow -18x=20$
$\Rightarrow x=-\frac{20}{18}$
$\Rightarrow x=-\frac{10}{9}$
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