$$\frac{2x+1}{x+4} = 2$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{2x+1}{x+4} &= 2&& \text{multiply ALL terms by } \color{blue}{ x+4 }. \\[1 em](x+4)\frac{2x+1}{x+4} &= (x+4)\cdot2&& \text{cancel out the denominators} \\[1 em]2x+1 &= 2x+8&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ 1 }$ to the right} \\[1 em]2x-2x &= 8-1&& \text{simplify left and right hand side} \\[1 em]2x-2x &= 7&& \\[1 em]0 &= 7&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 7 } $ is FALSE, we conclude that the equation has no solution.
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