Question

Solve the linear equation:

$\frac{x+2}{3}-\frac{x-3}{4}=5-\frac{x-1}{2}$

• A. $x=6$
• B. $x=4$
• C. $x=9$
• D. $x=7$

Answer 1

The correct option is D $x=7$

$Wehave,\frac{x+2}{3}-\frac{x-3}{4}=5-\frac{x-1}{2}⟹\frac{4(x+2)-3(x-3)}{12}=\frac{10-x+1}{2}\left[TakingLCMonLHSandRHS\right]⟹\frac{4x+8-3x+9}{12}=\frac{11-x}{2}⟹\frac{x+17}{6}=\frac{11-x}{1}\left[Onmultiplyingbothsidesby2\right]⟹x+17=6(11-x)[Bycross-multiplication]⟹x+17=66-6x⟹x+6x=66-17[Transposing-6xtoLHSand17toRHS]⟹7x=49⟹x=7$