Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

How do you solve for $ x $ in $ ax - c = b $ ?

Answer
VerifiedVerified
497.7k+ views
Hint: We can see that the given equation is a linear equation with one variable as the degree of the equation is $ 1 $ and only one variable is present in the equation which is $ x $ . When we are given such equation to solve, it means we have to find the value of $ x $ by shifting all the terms without the variable $ x $ to the RHS, while keeping all the terms with the variable $ x $ in the LHS and then equating them will give us the value of $ x $ .

Complete step-by-step answer:
(i) The equation given to us is:
 $ ax - c = b $
Since it has only one variable present in it and the degree of the equation is $ 1 $ as the highest power of the variable $ x $ is $ 1 $ , we can say that it is a linear equation with one variable. Solving an equation with one variable is the same as calculating the value of the variable i.e., $ x $ .
Therefore, we have to shift all the terms containing the variable $ x $ to LHS and the rest of the terms to RHS. Since, here only one term contains $ x $ which is already in LHS, we will just shift the rest to RHS.
So, adding $ c $ on both the sides, we will get:
 $ ax - c + c = b + c $
Simplifying it further, we will get:
 $ ax = b + c $
(ii) Now, dividing both the sides by $ a $ , we will get:
 $ \dfrac{{ax}}{a} = \dfrac{{b + c}}{a} $
On simplifying, it will become:
 $ x = \dfrac{{b + c}}{a} $
Hence, $ ax - c = b $ when solved for $ x $ gives $ x = \left( {\dfrac{{b + c}}{a}} \right) $
So, the correct answer is “ $ x = \left( {\dfrac{{b + c}}{a}} \right) $ ”.

Note: Always remember that in questions like this, our approach should be to keep the variable $ x $ in LHS, and rest everything in RHS to isolate $ x $ because this is how we will find the value of $ x $ . Also, note that the sign of the term changes when we shift that term from one side to the other. For example, when we shifted $ - c $ from LHS to RHS in the first step, it changed it sign and became $ + c $
WhatsApp Banner