Question

A numerator of a fraction is thrice of the denominator and plus 7. The fraction equals to $\frac{2}{3}$. Find the value of $\text{x}$.

• A. $\frac{2}{3}$
• B. $-\frac{2}{3}$
• C. $-3$
• D. 3

Answer 1

The correct option is A $\frac{2}{3}$

Let the denominator be $\text{x}$.
Numerator of the fraction is thrice the denominator and plus 7.
$\Rightarrow$ Numerator = 3x + 7

Given, the fraction is equals to $\frac{2}{3}$.

$\Rightarrow \frac{\text{3x + 7}}{\text{x}}=\frac{2}{3}$

$\Rightarrow \left(3\text{x}+7\right)\times 3=2\times \left(\text{x}\right)$

$\Rightarrow 9\text{x}+21=2\text{x}$

$\Rightarrow 9\text{x}-2\text{x}=-21$

$\Rightarrow 7\text{x}=-21$

$\Rightarrow \text{x}=-3$