Question
$$v-\frac{6}{5} = v+\frac{10}{2}$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} v-\frac{6}{5} &= v+\frac{10}{2}&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10v-10\cdot\frac{6}{5} &= 10v+10\cdot\frac{10}{2}&& \text{cancel out the denominators} \\[1 em]10v-12 &= 10v+50&& \text{move the $ \color{blue}{ 10v } $ to the left side and $ \color{blue}{ -12 }$ to the right} \\[1 em]10v-10v &= 50+12&& \text{simplify left and right hand side} \\[1 em]10v-10v &= 62&& \\[1 em]0 &= 62&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 62 } $ is FALSE, we conclude that the equation has no solution.
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