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