Question

If $\frac{5x}{3}–4=\frac{2x}{5}$, then the numerical value of $2x–7$ is

• A. $\frac{19}{13}$
• B. $\frac{-13}{19}$
• C. $0$
• D. $\frac{13}{19}$

Answer 1

The correct option is B

$\frac{-13}{19}$

Solve the given expression

Given,

$\Rightarrow \frac{5x}{3}–4=\frac{2x}{5}$

$\Rightarrow \frac{5x}{3}-\frac{2x}{5}=4$

$\Rightarrow \frac{5\left(5x\right)-3\left(2x\right)}{15}=4$

$\Rightarrow \frac{25x-6x}{15}=4$

$\Rightarrow \frac{19x}{15}=4$

$\Rightarrow x=\frac{4\times 15}{19}$

$\Rightarrow x=\frac{60}{19}$

Now, put this value of $x$ in $2x–7$, we get,

$$\begin{gathered} 2x–7=2\left(\frac{60}{19}\right)-7 \\ =\frac{120-133}{19} \\ =\frac{-13}{19} \end{gathered}$$

Hence, the given expression is $\frac{-13}{19}$, so, option (b) is the correct answer.