Question

How do you write \[3x+9=\dfrac{7}{2}y\] in standard form?

Answer 1

Hint: In the question that has been mentioned above we have been given an equation in which some of the variables are in fraction form which cannot be stated as standard form so we need to remove the fraction and write the equation in standard form.

Complete step by step answer:
In the above mentioned question we need to write the standard form of a linear equation which is :
\[ax+by=c\]
We need to write the given equation in the same format as mentioned above for this we are going to first multiply the whole equation by 2 to remove the fraction part in the right hand side of the equation, by multiplying 2 on both the sides of the equation we will get:
\[\begin{align}
  & \Rightarrow 2\left( 3x+9 \right)=2\left( \dfrac{7}{2}y \right) \\
 & \Rightarrow 6x+18=7y \\
\end{align}\]
Now after multiplying 2 on both sides we got rid of the fraction on right hand side of the equation, now when we observe the standard form of the linear equation we can clearly see that all the variables are present on the left side of the equation and the constants are to present on the right side of the equation and by doing that we can convert our equation to standard form of linear equation.
So to convert our linear equation into standard equation we need to shift the y variable towards the left side of the equation and the constant value to the right side of the equation and we will get it as:
\[6x-7y=-18\]
So the standard form of the equation given in the question is \[6x-7y=-18\].

Note:
For solving this type of question we need to first know about the standard form of the different kinds of equation after having an understanding of all the standard forms we can convert any kind of equation into its standard form with ease and without trouble.