Question

10x=-80, x=?, solve using multiplication principle

Answer 1

The idea behind this is that every element of the field has a multiplicative inverse.

Answer 2

\[10x\cdot10^{-1} = 10x\cdot\frac{1}{10} = -80 \cdot \frac{1}{10}\]

Answer 3

Now applying commutativity of multiplication we have
\[\frac{10}{10} \cdot x = \frac{-80}{10}\]\[x = -8\]

Answer 4

Is that the so called "multiplication principle" math teachers talk about?

Answer 5

Or you could note that 10 *x = 10*-8...