Question

The solution of the equation \[ax - b = 0\] is
A.\[\dfrac{a}{b}\]
B. \[\dfrac{{ - a}}{b}\]
C. \[\dfrac{{ - b}}{a}\]
D. \[\dfrac{b}{a}\]

Answer 1

Hint: We use the given linear equation in one variable and use arithmetic operations like addition, subtraction, multiplication and division to calculate the solution of the equation.
* Solution of any linear equation in one variable is that value of the variable that gives the value of the equation as zero.

Complete step-by-step solution:
We are given linear equation in one variable \[ax - b = 0\]............… (1)
We have to find solution of equation (1)
\[ \Rightarrow \]We have to find the value of ‘x’ such that the left hand side of the equation becomes equal to the right hand side of the equation.
We equate left hand side of the equation becomes to right hand side of the equation
\[ \Rightarrow ax - b = 0\]
Shift all variables except those along with variable ‘x’ along them to right hand side of the equation
\[ \Rightarrow ax = b\]
Divide both sides of the equation by ‘a’
\[ \Rightarrow \dfrac{{ax}}{a} = \dfrac{b}{a}\]
Cancel same terms from numerator and denominator in left hand side of the equation
\[ \Rightarrow x = \dfrac{b}{a}\]
So, the value of \[x = \dfrac{b}{a}\].
\[\therefore x = \dfrac{b}{a}\] is solution of the equation \[ax - b = 0\]

\[\therefore \]Correct option is D.

Note: Many students make mistakes when they don’t change the sign of the values when shifting a value from one side of the equation to the opposite side of the equation. Keep in mind we always change the sign of the value from positive to negative and vice-versa when shifting the value from one side of the equation to another.
Also, keep in mind the sign of the answer plays an important role in being a solution of a linear equation, so carefully choose the option that matches both the magnitude and the sign of the obtained solution.