Question Number 213099 by MathematicalUser2357 last updated on 30/Oct/24
$$\frac{\mathrm{1}}{\mathrm{2}}\left({x}−\mathrm{1}\right)−\left({x}−\mathrm{3}\right)=\frac{\mathrm{1}}{\mathrm{3}}\left({x}+\mathrm{3}\right)+\frac{\mathrm{1}}{\mathrm{6}} \\ $$$${x}=… \\ $$
Answered by MrGaster last updated on 30/Oct/24
$$\frac{\mathrm{1}}{\mathrm{2}}{x}−\frac{\mathrm{1}}{\mathrm{2}}−{x}+\mathrm{3}=\frac{\mathrm{1}}{\mathrm{3}}{x}+\mathrm{1}+\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}{x}+\frac{\mathrm{5}}{\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}}{x}+\frac{\mathrm{7}}{\mathrm{6}} \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}{x}−\frac{\mathrm{1}}{\mathrm{3}}{x}=\frac{\mathrm{7}}{\mathrm{6}}−\frac{\mathrm{5}}{\mathrm{2}} \\ $$$$−\frac{\mathrm{3}}{\mathrm{6}}{x}−\frac{\mathrm{2}}{\mathrm{6}}{x}=−\frac{\mathrm{4}}{\mathrm{6}} \\ $$$$−\frac{\mathrm{5}}{\mathrm{6}}{x}=\frac{\mathrm{8}}{\mathrm{6}} \\ $$$${x}=\frac{−\frac{\mathrm{8}}{\mathrm{6}}}{−\frac{\mathrm{5}}{\mathrm{6}}} \\ $$$${x}=\frac{\mathrm{8}}{\mathrm{5}} \\ $$