Question

Find the correct error of the following mathematical expression.
 $ 4(x - 5) = 4x - 5 $

Answer 1

Hint: Multiplication is distributive over addition and subtraction. That means, when we open any bracket, then the term, that was in multiplication with the bracket, gets multiplied to all the terms which were in addition or subtraction to each other, inside the bracket.

Complete step-by-step answer:
Multiplication is distributive over addition and subtraction.
Mathematically, it is written as,
 $ a(b \pm c) = ab \pm ac $
That means, when we open any bracket, then the term, that was in multiplication with the bracket, gets multiplied to all the terms which were in addition or subtraction to each other, inside the bracket.
Therefore, by using the distributive law of multiplication, over subtraction, we can write
 $ 4(x - 5) = 4x - 4 \times 5 $
 $ \Rightarrow 4(x - 5) = 4x - 20 $
But the RHS in the above equation is not equal to the RHS in the question. i.e.
 $ 4x - 20 \ne 4x - 5 $
Therefore, RHS in the equation given in the question is incorrect. And the error is the term $ 5 $
Therefore, from the above explanation, we can say that the error in the given mathematical expression in the question is the term $ 5 $ in the RHS. And it could be corrected by writing $ 20 $ instead of $ 5 $ .

Note: It is a basic law in algebra. We use it many times, but don’t know the name or the definition of the law. It would be better if you give more attention to such laws. But for this question, the answer was easy to be found by just opening the bracket. Be careful with the sign of the terms inside the bracket.