Question

What is the standard form of linear equation in one variable?

Answer 1

Hint: We explain this problem by taking the equation of linear equation in one variable.
The linear equation of one variable is an equation having only one variable in the equation and the power of that variable should be one because of linearity.
We define the function in such a way and find the solution for that equation.

Complete step by step answer:
We are asked to give the standard form of a linear equation of one variable.
Here we can see that the name suggests that the equation has one variable and it should be linear.
We know that the linear equation of one variable is an equation having only one variable in the equation and the power of that variable should be one because of linearity.
By using the above condition we can have the standard form of the linear equation as
\[\Rightarrow ax+b=0\]
Where, \[a,b\] are constants and \[a\ne 0\]
Now, let us find the solution to this standard form of an equation.
Now, let us subtract the equation with \[b\] on both sides then we get
\[\begin{align}
  & \Rightarrow ax+b-b=0-b \\
 & \Rightarrow ax=-b \\
\end{align}\]
Now, by dividing the above equation with \[a\] we get
\[\begin{align}
  & \Rightarrow \dfrac{ax}{a}=\dfrac{-b}{a} \\
 & \Rightarrow x=\dfrac{-b}{a} \\
\end{align}\]
Therefore we can conclude that the standard form of linear equation of one variable is given as
\[\Rightarrow ax+b=0\]
Where, \[a,b\] are constants and \[a\ne 0\]
Also we can conclude that the solution of that standard form of linear equation of one variable is given as \[x=\dfrac{-b}{a}\]

Note:
 We need to keep in mind that in the standard equation the coefficient of the variable should not be equal to 0.
We have the standard form of the linear equation of one variable as
\[\Rightarrow ax+b=0\]
Where, \[a,b\] are constants and \[a\ne 0\]
Here the condition \[a\ne 0\] is very important.
Suppose if \[a=0\] then the equation becomes as
\[\Rightarrow b=0\]
Here we can see that there is no variable at all which is not called a linear equation of one variable.