Question
$$5x-3 = 6(x+1)$$
Answer
$$ x = -9 $$
Explanation
$$ \begin{aligned} 5x-3 &= 6(x+1)&& \text{simplify right side} \\[1 em]5x-3 &= 6x+6&& \text{move the $ \color{blue}{ 6x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]5x-6x &= 6+3&& \text{simplify left and right hand side} \\[1 em]-x &= 9&& \text{switch signs on both sides} \\[1 em]x &= -9&& \\[1 em] \end{aligned} $$
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