$$ \begin{aligned} 4x+3 &= x&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]4x-x &= -3&& \text{simplify left side} \\[1 em]3x &= -3&& \text{ divide both sides by $ 3 $ } \\[1 em]x &= -\frac{3}{3}&& \\[1 em]x &= -1&& \\[1 em] \end{aligned} $$