Notate the absolute value problem given on your paper or computer. The absolute value of -2, for instance, becomes abs(-2) or |-2|, while a more complex absolute value expression is abs(-5 + 3) or |-5 + 3|.
Simplify the absolute value to evaluate the meaning. Work the math inside the pipes only, using the order of operations inside the pipes as you would inside parentheses. So |-5 + 3| translates into |-2|.
Determine the absolute value of the evaluated expression. Absolute value indicates the spaces from "0" on a number bar and can never be a negative number. For example, |-2| transforms into "2."
Design a number line to help visualize the results: <---- -2 ----- 0 ----- 2 ----> Notice that whether you determine the distance from -2 to 0, or 0 to +2, the answer remains the same -- the distance is 2. Thus, the absolute value of -2 (or any math problem inside the absolute value sign that equals 2 or -2) is always 2.
Calculate any absolute value expression, no matter how complex, similarly. The only thing to remain aware of is that values outside the absolute value sign are not applied until the absolute value expression itself is determined. Thus, given the problem -| -2 |, first evaluate the inside of the pipes, then convert the pipes to parentheses and carry the numbers or instructions outside the pipes: -|-2| = -(+2). Process in terms of math rules, carrying the negative into the number in parentheses to obtain -2 (the opposite of the absolute value given.)