Question
$$\frac{3}{2}(-\frac{56}{5})+8 = \frac{1}{4}(-\frac{56}{5})-6$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} \frac{3}{2}(-\frac{56}{5})+8 &= \frac{1}{4}(-\frac{56}{5})-6&& \text{multiply ALL terms by } \color{blue}{ 20 }. \\[1 em]20 \cdot \frac{3}{2}(-\frac{56}{5})+20\cdot8 &= 20 \cdot \frac{1}{4}(-\frac{56}{5})-20\cdot6&& \text{cancel out the denominators} \\[1 em]-336+160 &= -56-120&& \text{simplify left and right hand side} \\[1 em]-176 &= -176&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ -176 = -176 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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