\(\dfrac{x-2}{3}=\dfrac{x+1}{4}\\ \Rightarrow\dfrac{4\left(x-2\right)}{12}=\dfrac{3\left(x+1\right)}{12}\\ \Rightarrow4x-8=3x+3\\ \Rightarrow x=11\)
\(\dfrac{x-2}{3}=\dfrac{x+1}{4}\\ \Rightarrow\left(x-2\right)\cdot4=\left(x+1\right)\cdot3\\ \Rightarrow4x-8=3x+3\\ \Rightarrow4x-3x=-8+3\\ \Rightarrow x=-5\)
\(\dfrac{x-2}{3}=\dfrac{x+1}{4}\\ \Rightarrow\left(x+2\right)\cdot4=\left(x+1\right)\cdot3\\ \Rightarrow4x+8=3x+3\\ \Rightarrow4x-3x=8+3\\ \Rightarrow x=11\)