<s>[INST] Multiplying the denominator $$\frac{2}{3} \gt -4y - \frac{25}{3}$$
My question is to solve this problem we need to multiply both sides by $3$. The result will be 
$$2 \gt -12y - 25.$$
Why doesn't the numerator of both $\frac{2}{3}$ and $\frac{25}{3}$ get multiplied?
 [/INST] $$\begin{align}
\frac{2}{3}
&>
-4y-\frac{25}{3} \\
3\left(\frac{2}{3}\right)
&>
3\left(-4y-\frac{25}{3}\right) \\
3·\frac{2}{3}
&>3·\left(-4y\right)-3·\frac{25}{3} \\
\require{cancel} \cancel{3}·\frac{2}{\require{cancel} \cancel{3}} 
&>
3·\left(-4y\right) -\require{cancel} \cancel{3} ·\frac{25}{\require{cancel} \cancel{3}} \\
2
&>
-12y -25 \\
\end{align}$$
</s>