Question

Solve the equation: $5 - \dfrac{{2d + 7}}{9} = 0$

Answer 1

Hint: In the given problem, we are required to find the value of the variable d in the given equation $5 - \dfrac{{2d + 7}}{9} = 0$. We can solve the given equation using the method of transposition. Method of transposition involves doing the exact same mathematical thing on both sides of an equation with the aim of simplification in mind. We will shift the term from one side to the equation to another with the objective of isolating the variable d.

Complete step-by-step solution:
We would use the method of transposition to find the value of d in the given equation $5 - \dfrac{{2d + 7}}{9} = 0$.
Method of transposition involves doing the exact same thing on both sides of an equation with the aim of bringing like terms together and isolating the variable or the unknown term in order to simplify the equation and finding the value of the required parameter.
Now, in order to find the value of h, we need to isolate d from the rest of the parameters such as the constant terms.
So, $5 - \dfrac{{2d + 7}}{9} = 0$
Firstly, we put the rational term consisting of the variable d in a bracket to avoid the calculation mistakes while solving the equation and shifting of the terms.
$ \Rightarrow $$5 - \left( {\dfrac{{2d + 7}}{9}} \right) = 0$
Now, we shift the entire bracket to the right side of the equation,
$ \Rightarrow $$5 = \left( {\dfrac{{2d + 7}}{9}} \right)$
Multiplying both sides of the equation, we get,
$ \Rightarrow $$5 \times 9 = 2d + 7$
Changing the sides of equation,
$ \Rightarrow $$2d + 7 = 5 \times 9$
Simplifying the calculations,
$ \Rightarrow $$2d + 7 = 45$
Shifting all the constant terms to the right side of the equation,
$ \Rightarrow $$2d = 45 - 7$
$ \Rightarrow $$2d = 38$
Dividing both sides of the equation by $2$, we get,
Hence, the value of d in the equation given to us in the problem, $5 - \dfrac{{2d + 7}}{9} = 0$ is $19$.
Therefore, option (A) is the correct answer.

Note: There is no fixed way of solving a given algebraic equation. Algebraic equations can be solved in various ways. Linear equations in one variable can be solved by the transposition method with ease. We must take care while cancelling the common factors in numerator and denominator so as to get to the final answer. Also, utmost care should be taken while shifting the terms from one side of the equation to another as we have to reverse the signs of the terms.