Question
$$\frac{2x-3}{4} = \frac{x+5}{2}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} \frac{2x-3}{4} &= \frac{x+5}{2}&& \text{multiply ALL terms by } \color{blue}{ 4 }. \\[1 em]4 \cdot \frac{2x-3}{4} &= 4 \cdot \frac{x+5}{2}&& \text{cancel out the denominators} \\[1 em]2x-3 &= 2x+10&& \text{move the $ \color{blue}{ 2x } $ to the left side and $ \color{blue}{ -3 }$ to the right} \\[1 em]2x-2x &= 10+3&& \text{simplify left and right hand side} \\[1 em]2x-2x &= 13&& \\[1 em]0 &= 13&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 13 } $ is FALSE, we conclude that the equation has no solution.
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