Question
$$7v+42 = 11(3v+8)-2(13v-1)$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 7v+42 &= 11(3v+8)-2(13v-1)&& \text{simplify right side} \\[1 em]7v+42 &= 33v+88-(26v-2)&& \\[1 em]7v+42 &= 33v+88-26v+2&& \\[1 em]7v+42 &= 7v+90&& \text{move the $ \color{blue}{ 7v } $ to the left side and $ \color{blue}{ 42 }$ to the right} \\[1 em]7v-7v &= 90-42&& \text{simplify left and right hand side} \\[1 em]7v-7v &= 48&& \\[1 em]0 &= 48&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = 48 } $ is FALSE, we conclude that the equation has no solution.
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