Question

How do you solve $ 4{m^2} = 4m $ ?

Answer 1

Hint: Here first of all we will take the given expression, will bring all the terms on one side of the equation and will take out the common multiple and then solve for the required resultant value for “m”.

Complete step by step solution:
Take the given expression: $ 4{m^2} = 4m $
Take the term from the right hand side of the equation to the left hand side of the equation. When you move any term from one side to another, the sign of the term also changes. Positive terms become negative and vice-versa.
 $ 4{m^2} - 4m = 0 $
Take the common multiple common from both the terms in the above equation.
 $ 4m(m - 1) = 0 $
The above equation gives two values-
 \[ \Rightarrow 4m = 0\] or $ \Rightarrow m - 1 = 0 $
Case (I) $ 4m = 0 $
When the term multiplicative on one side is moved to the opposite side, then it goes to the denominator.
 $ \Rightarrow m = \dfrac{0}{4} $
Any number upon zero is always zero.
 $ \Rightarrow m = 0 $
Case (II) $ m - 1 = 0 $
Move constant from left to the right hand side of the equation. When you move any term from one side to another then the sign of the term also changes. Negative terms become positive and vice-versa.
 $ m = 1 $
Hence, we get $ m = 0 $ or $ m = 1 $
So, the correct answer is “ $ m = 0 $ or $ m = 1 $ ”.

Note: Be careful about the sign convention while simplification of the terms. Always remember when you move any term from one side to another, then the sign of the term also changes. Positive term becomes the negative term and the negative term becomes the positive term. Always remember zero multiplied with any number gives zero as the value and any number upon zero gives zero as the value.