Question

How do you solve the equation for \[y:\dfrac{2x}{5}-\dfrac{x}{3}=3\]?

Answer 1

Hint: In this problem, we have to solve and find the value of x for the given equation. We can first analyse the given equation. We can see that the equation does not have a similar denominator, so we can cross multiply the terms on the left-hand side and we can add or multiply terms on both the left-hand side and the right-hand side of the equation to get the value of x.

Complete step-by-step solution:
We know that the given equation is,
\[y:\dfrac{2x}{5}-\dfrac{x}{3}=3\]
We can see that the equation does not have similar denominator, so we can cross multiply the terms on the left-hand side and we can multiply the terms in the denominator to get a common denominator, we get
\[\Rightarrow \dfrac{2x\times 3-5x}{3\times 5}=3\]
We can now simplify the above step, we get
\[\Rightarrow \dfrac{6x-5x}{15}=3\]
We can now subtract the numerator, we get
\[\Rightarrow \dfrac{x}{15}=3\]
We can now multiply the number 5 on both the left-hand side and the right-hand side of the equation, we get
\[\begin{align}
  & \Rightarrow x=3\times 15 \\
 & \Rightarrow x=45 \\
\end{align}\]
Therefore, the value of \[x=45\].

Note: Students make mistakes while cross multiplying the terms, where we have to multiply the term in the numerator of one side to the term in the denominator of other side to the numerator and we have to multiply the individual denominator to make a common denominator. We can simplify the step to get the value of x.