$$7x+1 = 8x+14$$
Answer
$$ x = -13 $$
Explanation
$$ \begin{aligned} 7x+1 &= 8x+14&& \text{move the $ \color{blue}{ 8x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]7x-8x &= 14-1&& \text{simplify left and right hand side} \\[1 em]-x &= 13&& \text{switch signs on both sides} \\[1 em]x &= -13&& \\[1 em] \end{aligned} $$
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