Question

How do you solve \[\dfrac{3}{5}x=\dfrac{7}{10}\]?

Answer 1

Hint: We know that, to solve a linear equation, we need to take all the variable terms to one side of the equation and constants to the other side of the equation. We will do the same for the given equation also. The given equation already has all variable terms and constant terms on different sides of the equation. So, we just have to make the coefficient of variable term one by multiplying or dividing it by some constants.

Complete step by step solution:
The equation we are asked to solve is \[\dfrac{3}{5}x=\dfrac{7}{10}\]. As we can see that the degree of this equation is one. Hence, it is a linear equation. We know that to solve a linear equation, we need to take all the variable terms to one side of the equation and constants to the other side of the equation. We will do the same for the given equation also.
The given equation already has all the variable terms to one side, and the constant terms to the other side
\[\dfrac{3}{5}x=\dfrac{7}{10}\]
Multiplying both sides of the equation by \[\dfrac{5}{3}\], we get
\[\Rightarrow \dfrac{5}{3}\left( \dfrac{3}{5}x \right)=\dfrac{5}{3}\left( \dfrac{7}{10} \right)\]
Simplifying above equation, we get
\[\Rightarrow x=\dfrac{7}{6}\]
Thus, the solution of the given equation is \[x=\dfrac{7}{6}\].

Note: For this problem, the equation already had constant and variable terms on different sides. But, this will not always be true. For a general linear equation, we have to take the variable terms on one side, and the constant term to the other side. Then, make the coefficient one, and find its solution value.