Answers

Check out the PrepMe SAT lesson entitled "Advanced Apples." It explains absolute values and algebra using absolute values; it also has some tips and details that may help you understand better what's going on.

If you're in the ACT course, check out the lessons entitled "Absolute Values" and "Absolute Value Equations and Inequalities."

The absolute value of a real number is just its numerical value without regard to its sign (positive or negative). This means the value of an absolute value is always positive. For example, the absolute value of -5 is 5. This is written |-5| = 5. And to solve the other way, a number with an absolute value of 17 could either be 17 or -17.

Think of it this way: If you put ANY number in between the absolute value signs, the number will always come out positive. When I say any number, I am talking about positive, negative, decimal or fraction.

The concept of an absolute value is fairly easy to understand, but when absolute values are put into functions and algebraic equations, things get a little more complicated. Solving these kinds of equations requires rote knowledge of algebra and a good conceptual understanding of absolute values.

I recommend just going through your math textbook, reading the explanation of absolute values, and then practicing as many of the examples as you can. Most textbooks have the answers for half the problems in the back, so you can check your answers against them.