Question

How do you solve \[\dfrac{7}{4}=\dfrac{r}{5}\]?

Answer 1

Hint: Cross – multiply the numerator of one side of the equation with the denominator of the other side of the equation to simplify the expression. Now, rearrange the terms by taking the terms containing the variable ‘r’ to the L.H.S. while taking the constant terms to the R.H.S. To solve the equation for the value of r make its coefficient equal to 1 and accordingly to change the R.H.S. to get the answer.

Complete step by step solution:
Here, we have been provided with the equation: \[\dfrac{7}{4}=\dfrac{r}{5}\] and we are asked to solve this equation, that means we have to find the value of r.
Clearly, we can see that the given equation is a linear equation in one variable which is ‘r’, so now cross – multiplying the numerator of one side of the equation with the denominator of the other side of the equation, we get,
\[\begin{align}
  & \Rightarrow 7\times 5=4\times r \\
 & \Rightarrow 35=4r \\
\end{align}\]
Now, taking the terms containing the variable ‘r’ to the L.H.S. while taking the constant terms to the R.H.S., we get,
\[\Rightarrow 4r=35\]
To solve the equation for the value of r means we have to make the coefficient of r equal to 1. For this we have to divide both the sides with 4, so we get,
\[\Rightarrow r=\left( \dfrac{35}{4} \right)\]
Hence, the value of r is \[\left( \dfrac{35}{4} \right)\].

Note: One may note that here we have considered the given equation as a linear equation because after simplifying the equation we can clearly see that the exponent of r is 1. Once can check the answer by substituting the obtained value of r in the original equation. We will solve L.H.S. and R.H.S. separately and if they are equal then our answer is correct. Note that here we have only one variable and that is why we were provided with only one equation.