Question

How do you solve $\dfrac{3x}{4x}=\dfrac{3x+7}{5x-8}$ ?

Answer 1

Hint: We have been given an equation in fractional format. The right hand side of the equation consists of a fraction whose numerator and denominator both consist of a linear equation in one variable. We shall start by simplifying the equation given to us. Then we shall cross multiply the terms on the left hand side and right hand to solve the equation further.

Complete step by step solution:
Given that $\dfrac{3x}{4x}=\dfrac{3x+7}{5x-8}$. In order to obtain the solution of this equation, we shall find out the value of variable $x$.
We see that the x-variable on the left hand side of the equation is present in the numerator as well as in the denominator. Thus, we shall cancel the x-variable term.
$\Rightarrow \dfrac{3}{4}=\dfrac{3x+7}{5x-8}$
Now, we will cross-multiply the remaining terms to form a proper equation without fractions.
$\Rightarrow 3\left( 5x-8 \right)=4\left( 3x+7 \right)$
Opening the brackets and multiplying the respective terms, we get
$\Rightarrow 15x-24=12x+28$
Here, we will transpose all the terms with x-variable to the left-hand side and all the constant terms to the right-hand side.
$\Rightarrow 15x-12x=28+24$
$\Rightarrow 3x=52$
On dividing both sides by 3 to make the coefficient of x equal to 1, we get
$\Rightarrow x=\dfrac{52}{3}$
Thus, we have obtained the value of x equal to $\dfrac{52}{3}$.

Therefore, the solution of $\dfrac{3x}{4x}=\dfrac{3x+7}{5x-8}$ is $x=\dfrac{52}{3}$.

Note: This equation could have been solved by another method which was to directly cross-multiply the terms without cancelling the common terms. However, this would have led us to the formation of two quadratic equations to be simplified whose 2-degree would later get cancelled while getting transposed. This method would have only made the solution more calculative and lengthier, hence we tend to avoid it.