Q58. - Algebra 1

Question

Explain whether 1 can be an additive identity. Give an example to justify your answer.

Step-by-Step Solution

Answer

1 can never be an additive identity.

Step 1. Additive identity.

Additive identity:

A number ‘a’ is additive identity if for any number ‘x’ 

$a+x=x+a=x$

Step 2. DESCRIPTION OF STEP.

Now let 1 is additive identity than for any number x

$\begin{array}{l}1+x=x\\ \Rightarrow 1=x-x\\ \Rightarrow 1=0\end{array}$

But this is a contradiction.

Thus, 1 can never be an additive identity.