$$3x+1 = 4x-6$$
Answer
$$ x = 7 $$
Explanation
$$ \begin{aligned} 3x+1 &= 4x-6&& \text{move the $ \color{blue}{ 4x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]3x-4x &= -6-1&& \text{simplify left and right hand side} \\[1 em]-x &= -7&& \text{switch signs on both sides} \\[1 em]x &= 7&& \\[1 em] \end{aligned} $$
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