Question

How do you solve \[\dfrac{3}{7}=\dfrac{x-2}{6}\]?

Answer 1

Hint: The given expression is of the form \[\dfrac{a}{b}=\dfrac{c}{d}\]. To solve these types of expressions, we need to first convert it to an equation of appropriate degree. As we can see the variable term with the highest power in the given expression is x. So, it will form a one variable linear equation on rearranging the terms. We know the standard steps to solve a one variable linear equation.

Complete step by step solution:
We are given the equation \[\dfrac{3}{7}=\dfrac{x-2}{6}\], we have to solve it. The highest power of the variable of the equation is 1, so the degree of the equation is also one. Hence, it is a linear equation. As we know to solve a linear equation, we have to take all the variable terms to one side of the equation and leave constants to the other side.
\[\dfrac{3}{7}=\dfrac{x-2}{6}\]
Multiplying the above equation by 6 to both sides and cancelling out the common factors, we get
\[\begin{align}
  & \Rightarrow 6\left( \dfrac{3}{7} \right)=6\left( \dfrac{x-2}{6} \right) \\
 & \Rightarrow \dfrac{18}{7}=x-2 \\
\end{align}\]
Flipping the above equation, we get
\[\Rightarrow x-2=\dfrac{18}{7}\]
Adding 2 to both sides of the above equation, we get
\[\begin{align}
  & \Rightarrow x=\dfrac{18}{7}+2=\dfrac{32}{7} \\
 & \therefore x=\dfrac{32}{7} \\
\end{align}\]
Hence, the solution of the given equation is \[x=\dfrac{32}{7}\].

Note: We can check if the answer is correct or not by substituting the value in the given equation. From the given equation, we get the left-hand side as \[\dfrac{3}{7}\], and the right-hand side as \[\dfrac{x-2}{6}\]. Substituting \[x=\dfrac{32}{7}\] in both sides of the equation, we get LHS as \[\dfrac{3}{7}\], and RHS as \[\dfrac{\dfrac{32}{7}-2}{6}=\dfrac{3}{7}\]. As \[LHS=RHS\], the solution is correct.