Can anyone help me with this?
"if x is an irrational number, is 2x rational or irrational? explain"
If $\displaystyle 2x$ were a rational number then there exist integers $\displaystyle a$ and $\displaystyle b$ such that:
$\displaystyle 2x=\frac{a}{b}$
but then:
$\displaystyle x=\frac{a}{2b}$
but that means $\displaystyle x$ is also rational.
So if $\displaystyle x$ is irrational $\displaystyle 2x$ must also be irrational as otherwise we have a contradiction (we would have $\displaystyle x$ both rational and irrational and that is not possible).
CB