Question
$$3+\frac{3}{2}x+4 = 4x-\frac{5}{2}x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} 3+\frac{3}{2}x+4 &= 4x-\frac{5}{2}x&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]2\cdot3+2 \cdot \frac{3}{2}x+2\cdot4 &= 2\cdot4x-2 \cdot \frac{5}{2}x&& \text{cancel out the denominators} \\[1 em]6+3x+8 &= 8x-5x&& \text{simplify left and right hand side} \\[1 em]3x+14 &= 3x&& \text{move the $ \color{blue}{ 3x } $ to the left side and $ \color{blue}{ 14 }$ to the right} \\[1 em]3x-3x &= -14&& \text{simplify left side} \\[1 em]3x-3x &= -14&& \\[1 em]0 &= -14&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -14 } $ is FALSE, we conclude that the equation has no solution.
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