Question
$$\frac{3}{7}+\frac{9}{14} = \frac{15}{14}$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} \frac{3}{7}+\frac{9}{14} &= \frac{15}{14}&& \text{multiply ALL terms by } \color{blue}{ 14 }. \\[1 em]14\cdot\frac{3}{7}+14\cdot\frac{9}{14} &= 14\cdot\frac{15}{14}&& \text{cancel out the denominators} \\[1 em]6+9 &= 15&& \text{simplify left side} \\[1 em]15 &= 15&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 15 = 15 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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