Q14. - Algebra 2

Question

Name the property illustrated by each equation or statement.

 

14. If $\left(\mathbf{r}\mathbf{+}\mathbf{s}\right)\mathbf{t}\mathbf{=}\mathbf{rt}\mathbf{+}\mathbf{st}$, then $\mathbf{rt}\mathbf{+}\mathbf{st}\mathbf{=}\left(\mathbf{r}\mathbf{+}\mathbf{s}\right)\mathbf{t}$.

Step-by-Step Solution

Answer

Property illustrated in the statement is symmetric property of equality.

Step 1 – Symmetric property of equality.

Symmetric property of equality states that, for any real numbers p and $q,$ if $p=q$, then $q=p$.

Step 2 – Description of step.

Apply symmetric property of equality to $\left(r+s\right)t=rt+st$.

 

$rt+st=\left(r+s\right)t$

Step 3 – Description of step.

From step 1 and step 2, it can be concluded that the property illustrated in the given statement is symmetric property of equality.

 

Therefore, symmetric property of equality is illustrated in the given statement.