Question

How do you solve $\dfrac{5}{6} = \dfrac{{7n + 9}}{9}$?

Answer 1

Hint: since the equations is in the form of proportions, first we will try to get both the variables or at least one variable out of the denominator. After this step keep the terms having n on one side and rest on the other side and use normal rules of addition and subtraction to get the final answer.

Complete step by step answer:
First of all we would rewrite the equation for easy calculations as follows
$\dfrac{{7n + 9}}{9} = \dfrac{5}{6}$
After this we will multiply on both the sides by 9
We get
$
  7n + 9 = \dfrac{5}{6} \times 9 \\
   \Rightarrow 7n + 9 = \dfrac{{15}}{2} \\
 $
now after this step we will keep terms containing n on one side and shift rest on the other sides.
Hence the above equation will become
$7n = \dfrac{{15}}{2} - 9$
Which upon solving will be
$
  7n = \dfrac{{15}}{2} - 9 \\
   \Rightarrow 7n = \dfrac{{15 - 9\left( 2 \right)}}{2} \\
   \Rightarrow 7n = \dfrac{{15 - 18}}{2} \\
   \Rightarrow 7n = \dfrac{{ - 3}}{2} \\
 $
Since we want to find the value of n we will divide both sides of the equation by 7
$n = \dfrac{{ - 3}}{{2 \times 7}}$
Solving it further we get
$n = \dfrac{{ - 3}}{{14}}$
Which is our final answer.

Note: The method shown in the solution is one way of solving the problem. In the other way you can actually cross multiply both the denominators to the numerators and then keep all the terms with n on one side and rest on the other side to arrive at the final answer. Both the methods present you with the same answer.