Absolute Value

Definition: The absolute value of a number x is the distance from x to zero on a number line, or |x|. The absolute value of a number is always positive.

When solving absolute value equations, we must consider both the negative solution and positive solution. For example, given |x| = 5, there are two solutions for which the value of x is 5 units away from zero:

|5| = 5 or |-5| = 5,

so x = 5 or x = -5.

This is the same as rewriting |x| = 5 as x = ±5.Screen Shot 2016-02-17 at 1.26.29 PM

Example: Find the absolute values of -27 and 35.

Solution:

Step 1: Take the numerical value without the sign.

|-27| = 27

|35| = 35

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