Algebra Facts
Common Types of Mistakes: Omitted Solutions |

Sometimes only one of two or more solutions to an equation are found and the other solution(s) are omitted from an answer. Take care especially with square roots.
Mistake:
Click to see the mistake in red. Click to remove the red highlighting. This equation has not one, but two solutions, one of which is 4. However, there's another number whose square is 16: Click to see a correct solution. Click to hide the correct solution.
Remember that the square root symbol √ denotes just the positive square root, so you have to explicitly indicate a negative square root. If you have studied trigonometric functions, then Example 2 reminds you to be careful when solving equations involving these periodic functions.
Mistake:
Click to see the mistake in red. Click to remove the red highlighting. This equation has not one, but an infinite number of solutions: Click to see a correct solution. Click to hide the correct solution.
(for k = ...,-3,-2,-1,0,1,2,3,...)
There are two problems with the mistake. The first is that there are
If your first step in solving this equation is to write x=sin
Make sure you find |

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