Question

A student solved the given equation and justified every step except one. What is the missing reason? A) Associative property of addition B) Commutative property of addition C) Multiplicative property of equality D) Distributive property of multiplication over addition

Answer 1

Given:

The statements and reasons to solve an equation.

To find:

The missing reason.

Solution:

If a, b and c are three real number, then

Associative property of addition : $(a+b)+c=a+(b+c)$

Commutative property of addition : $a+b=b+a$

Multiplicative property of equality : $a=b\Leftrightarrow ca=cb$

Distributive property of multiplication over addition : $a(b+c)=ab+ac$

In the given step, $(x+-3)+3$ is written as  $x+(-3+3)$.

It means, only parenthesis are changed, which is possible by Associative property of addition.

So, the missing reason is Associative property of addition.

Therefore, the correct option is A.