What’s the absolute value of -3? |-3| = 3 That was easy.
How about the absolute value of 3? |3|=3.
Now let’s try this brain teaser, the absolute value of what number is 3? i.e. |x|=3? well we already determined above that 3 and -3 both have the absolute value of 3. Therefore the solutions to |x|=3 are 3 and -3.
What’s my point? well my point is that absolute value equations will always have two solutions. Also we use the fact that opposite values (i.e. -3 and 3 for example) have the same absolute value. Let’s do some creative thinking here…
Consider | x + 1 | = 3 this absolute value equation is very similar to the one above but instead of x we have x + 1 inside the absolute value symbols. Don’t be tricked we know that the only two numbers that result in an absolute value of 3 after taking there absolute value are 3 and -3. Therefore x + 1 must be equal to 3 or -3. This little concept is the key to unlocking the solutions to absolute value equations…start with easy absolute value equations to see how this whole thing works! good luck- the steps below should help a lot.
some key topics that involve solving absolute value equations:
* linear equations
* quadratic equations
* SAT and ACT exams
* college prep math and science courses