Question

How do you solve $\dfrac{7}{3}=\dfrac{2x+5}{x}$ ?

Answer 1

Hint: We first replace the fractions by numbers, by cross-multiplying both the sides of the equation. Upon further simplification by bringing all the $x$ terms together and the arithmetic terms to another side, we get the solution to the given equation.

Complete step-by-step solution:
The given equation is
$\dfrac{7}{3}=\dfrac{2x+5}{x}$
Let us multiply both sides of the equation by $x$ . The equation thus becomes,
$\Rightarrow \dfrac{7x}{3}=2x+5$
We then multiply both sides of the equation by $3$ . The equation thus becomes,
$\Rightarrow 7x=3\times \left( 2x+5 \right)$
We apply distributive law to the right hand side of the above equation. The equation gets simplified to,
$\Rightarrow 7x=6x+15$
We now subtract $6x$ from both sides of the equation. The equation thus becomes,
$\Rightarrow 7x-6x=15$
We perform the subtraction on the left hand side of the equation. The equation thus becomes,
$\Rightarrow x=15$
Therefore, we can conclude that $x=15$ is the solution to the given equation.

Note: We must be very careful while shifting the terms from one side of the equation to another. Most of the mistakes that are made by students are over here. Students often overlook some of the terms and this often ends up in wrong answers. Another method to solve the given problem will be by using the graphical approach. Here, we draw lines and find their point of intersection. The abscissa of the point where they intersect is the solution to the given equation. Upon cross-multiplying the given equation, we get
$\begin{align}
  & 7x=3\times \left( 2x+5 \right) \\
 & \Rightarrow 7x=6x+15 \\
\end{align}$
We draw two lines, one with equation $y=7x$ and the other with $y=6x+15$ . The point where they intersect is $\left( 15,105 \right)$ . The abscissa being $15$ , the solution is $15$ .