Dividing by Fractions in Algebra

You can divide by a fraction by multiplying by its reciprocal (i.e.$\frac{a}{b}\xf7\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$). Given the equation $\frac{1}{2}x=5$, intuitively, you could either multiply both sides by two or divide both sides by $\frac{1}{2}$. Both of these solutions give the same result, $x=10$

My maths teacher says that, when showing your work, you can only multiply by two. Subjectively, this is simpler. Is this an accepted rule, or is it just personal preference?

P.S. One of my previous teachers did teach to divide by fractions in this case.

You can divide by a fraction by multiplying by its reciprocal (i.e.$\frac{a}{b}\xf7\frac{c}{d}=\frac{a}{b}\times \frac{d}{c}$). Given the equation $\frac{1}{2}x=5$, intuitively, you could either multiply both sides by two or divide both sides by $\frac{1}{2}$. Both of these solutions give the same result, $x=10$

My maths teacher says that, when showing your work, you can only multiply by two. Subjectively, this is simpler. Is this an accepted rule, or is it just personal preference?

P.S. One of my previous teachers did teach to divide by fractions in this case.