Question

Question 63

Solve the following:

$\frac{1}{2}(x+1)+\frac{1}{3}(x-1)=\frac{5}{12}(x-2)$

Answer 1

Given, $\frac{1}{2}(x+1)+\frac{1}{3}(x-1)=\frac{5}{12}(x-2)\Rightarrow \frac{x}{2}+\frac{1}{2}+\frac{x}{3}-\frac{1}{3}=\frac{5}{12}(x-2)\Rightarrow \frac{x}{2}+\frac{x}{3}-\frac{5x}{12}=\frac{1}{3}-\frac{1}{2}-\frac{5}{6}\Rightarrow \frac{6x+4x-5x}{12}=\frac{2-3-5}{6}\Rightarrow \frac{5x}{12}=\frac{-6}{6}\Rightarrow 5x\times 6=(-6)\times 12\Rightarrow x=\frac{(-6)\times 12}{5\times 6}\therefore x=\frac{-12}{5}$