$$ \begin{aligned} 4x+3 &= 3x+10&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 3 }$ to the right} \\[1 em]4x-3x &= 10-3&& \text{simplify left and right hand side} \\[1 em]x &= 7&& \\[1 em]x &= 7&& \\[1 em] \end{aligned} $$