Question

How do you solve for A in \[B=\dfrac{5}{7}\left( A-9 \right)\]?

Answer 1

Hint: In the given question, we have been asked to find the value of A and it is given that \[B=\dfrac{5}{7}\left( A-9 \right)\]. To solve this question we need to get ‘A’ on one side of the “equals” sign, and all the other numbers on the other side. To solve this equation for a given variable ‘A’, we have to undo the mathematical operations such as addition, subtraction, multiplication and division that have been done to the variables. In this way we get our required solution.

Complete step by step solution:
We have given that,
\[\Rightarrow B=\dfrac{5}{7}\left( A-9 \right)\]
Multiply both the sides of the equation by 7, we get
\[\Rightarrow B\times 7=\dfrac{5}{7}\left( A-9 \right)\times 7\]
Simplifying the above equation, we get
\[\Rightarrow 7B=5\left( A-9 \right)\]
Dividing both the sides of the equation by 5, we get
\[\Rightarrow \dfrac{7B}{5}=\dfrac{5}{5}\left( A-9 \right)\]
After simplifying the above equation, we get
\[\Rightarrow \dfrac{7B}{5}=A-9\]
Adding 9 to both the sides of the equation, we get
\[\Rightarrow \dfrac{7B}{5}+9=A-9+9\]
After simplifying the numbers, we get
\[\Rightarrow \dfrac{7B}{5}+9=A\]
\[\therefore A=\dfrac{7}{5}B+9\]
Thus the possible value of A is \[\dfrac{7}{5}B+9\].
It is the required solution.

Note: In the given question, no mathematical formula is being used; only the mathematical operations such as addition, subtraction, multiplication and division is used. Use addition or subtraction properties of equality to gather variable terms on one side of the equation and constant on the other side of the equation. Use the multiplication or division properties of equality to form the coefficient of the variable term equivalent to 1. The important thing to recollect about any equation is that the ‘equals’ sign represents a balance.