Question

If $2x-9=8x+18$, then $x$ is:

• A. a fraction.
• B. an integer.
• C. a rational number.
• D. none of the above.

Answer 1

Answer: (C)

a rational number.

Given, $2x-9=8x+18$.

Adding $9$ to both sides,
$⟹2x-9+9=8x+18+9$
$⟹2x=8x+27$.

Transposing $x$ terms to one side, we get,
$⟹8x-2x=-27$
$⟹6x=-27$

$\therefore x=\frac{-27}{6}$= $\frac{-9}{2}$.

Here, $x$ is in $\frac{p}{q}$ for, where $q\ne 0$ and $p$ & $q$ have no common factors.

Hence, $x$ is a rational number.

Therefore, option $C$ is correct.