"checking" process.

Question

There are times when the solution process uses a rule or property that has restrictions, or limits to it's application. the multiplication property of equality when multiplying both sides of a rational equation by terms involving variables. The possible solutions all needed to be checked in the original equation or against the restricted value. Something similar happens with radical equations. Explain which rule is used, provide an example, and show the "checking" process.

Answer 1

The word it's in the statement of the problem should NOT have an apostrophe.

 

When you divide out a common factor, you're implicitly assuming that factor is not zero.

When you square a radical equation in order to eliminate a square root (or other even index radical), you might (implicitly) be introducing an extraneous root, thus necessitating checking.

 

All solutions need to be checked against domain restrictions inherent in the ORIGINAL presentation of a problem.

 

Then, too, almost always you benefit by checking the answers--this might be the way to detect that you've made an error somewhere in the details leading to your supposed answer.