Q3. - Algebra 2

Question

Choose the term that best completes each sentence.

If $\mathbf{x}\mathbf{+}\mathbf{3}\mathbf{=}\mathbf{y}$, then $\mathbf{y}\mathbf{=}\mathbf{x}\mathbf{+}\mathbf{3}$ is an example of the (Transitive, Symmetric) property of equality.

Step-by-Step Solution

Answer

If $x+3=y$, then $y=x+3$ is an example of the symmetric property of equality.

Step 1 – Transitive property of equality.

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

Step 2 – Symmetric property of equality.

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

Step 3 – Description of step.

Apply symmetric property of equality to $x+3=y$.

$y=x+3$

Step 4 – 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.