Question

Find the solution to the equation $\frac{4x}{5}-\frac{7}{4}=\frac{x}{5}+\frac{x}{4}$.

• A. $5$
• B. $6$
• C. $7$
• D. $0$

Answer 1

The correct option is A $5$

Given, $\frac{4x}{5}-\frac{7}{4}=\frac{x}{5}+\frac{x}{4}$.

$\Rightarrow (\frac{4x}{5}-\frac{7}{4})=(\frac{x}{5}+\frac{x}{4})$

$\Rightarrow \left(\frac{(4\times 4x)-(7\times 5)}{20}\right)=\left(\frac{5x+4x}{20}\right)$ ... [Cross-multiplying the denominators]

$\Rightarrow \left(\frac{16x-35}{20}\right)=\left(\frac{9x}{20}\right)$

$\Rightarrow 16x-35=9x$.

Transposing $x$ terms to one side, we get,

$\Rightarrow 16x-9x=35$

$\Rightarrow 7x=35$

$\Rightarrow x=\frac{35}{7}=5$

$\therefore x=5$.

Hence, option $A$ is correct.