Chapter EP, Problem 1.3.6EP

To determine

To name: The property illustrated by the given statement.

Answer to Problem 1.3.6EP

The given statement illustrates the “Substitution Property of the Equality.”

Explanation of Solution

Given:

The given statement is “if $x+\left(4+5\right)=21$ , then $x+9=21$ .”

Calculation:

The following table shows the Property of real numbers with reference to any three variables a , b , and c .

Property	Symbol
Reflexive	For any real number $a$ , $a=a$
Symmetric	For all real number $a$ and $b$ , if $a=b$ then $b=a$
Transitive	For all real number $a$ and $b$ , if $a=b$ and $b=c$ then $a=c$
Substitution	If $a=b$ , then $a$ may be replaced by $b$ and $b$ may be replaced by $a$
Addition and subtraction	For any real number $a$ , $b$ and $c$ , if $a=b$ , then $a+c=b+c$ and $a-c=b-c$
Multiplication and division	For any real number $a$ , $b$ and $c$ , if $a=b$ , then, $a\times c=b\times c$ and $\frac{a}{c}=\frac{b}{c}$ where $c\ne 0$ .

By comparing the given statement with the above properties, it is observed that the given statement illustrate the “Substitution Property of the Equality.”

Therefore, the given statement illustrates the “Substitution Property of the Equality.”