Algebra - Solutions and Solution Sets

Show Mobile Notice Show All Notes Hide All Notes

Mobile Notice

You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best viewed in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (you should be able to scroll/swipe to see them) and some of the menu items will be cut off due to the narrow screen width.

Section 2.1 : Solutions and Solution Sets

Back to Problem List

4. Is \(w = - 2\) a solution to \(\frac{{{w^2} + 8w + 12}}{{w + 2}} = 0\)?

Show Solution

There really isn’t all that much to do for these kinds of problems. All we need to do is plug the given number into both sides of the equation and check to see if the right and left side are the same value.

Note that for this problem we don’t even really need to plug the value into the equation. We can see by a quick inspection that if we were to plug \(w = - 2\) into this equation we would have division by zero and we know that is not allowed.

Therefore, \(w = - 2\) is not a solution to this equation.

Be very careful with this kind of problem. If we had plugged \(w = - 2\) into the equation we’d have gotten zero in the numerator as well and we might be tempted to say that it is a solution to the equation. We’d be wrong however. Regardless of the value of the numerator, we would still have division by zero and that is just not allowed and so \(w = - 2\) will not be a solution to this equation.