TransWikia.com

Is $frac{1}{x} = 4$ strictly a linear equation (in one variable)?

Mathematics Asked by Ispring Quiz on December 20, 2020

$$frac1{x} = 4$$
If multiplied by $x$ both sides,
$$1 = 4x$$
Then it looks like linear equation in one variable. But is such multiplication by variable on both sides allowed?

One Answer

The two expressions are equivalent within the condition that $xneq 0$ indeed for $x=0$ we would obtain

  • $frac1{0} = 4$
  • $1=0$

which are undefined.

We can observe that as equations in the unknown $x$ they are equivalent in the sense that they lead to the same solution $x=frac14$.

Otherwise for the expressions $frac {x^3}{x}=1$ and $x^3=x$ are not equivalent as equations because $x=0$ is a solution for the second one but not for the first one.

Correct answer by user on December 20, 2020

Add your own answers!

Ask a Question

Get help from others!

© 2024 TransWikia.com. All rights reserved. Sites we Love: PCI Database, UKBizDB, Menu Kuliner, Sharing RPP