Question

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

Answer 1

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

LCM of $5$ and $2$ is $10$, therefore,

$\Rightarrow \frac{2(2x+7)-5(3x+11)}{10}=\frac{2x+8-3\left(5\right)}{3}$

$\Rightarrow \frac{4x+14-15x-55}{10}=\frac{2x+8-15}{3}$

$\Rightarrow \frac{-11x-41}{10}=\frac{2x-7}{3}$

$\Rightarrow 3(-11x-41)=10(2x-7)$

$\Rightarrow -33x-123=20x-70$

$\Rightarrow -33x-20x=123-70$

$\Rightarrow -53x=53$

$\Rightarrow x=-1$

Therefore $x=-1$