## LinearAbsoluteValue

#### Linear Absolute Value Equations and Inequalities

Recall the definition of the absolute value of X : Therefore, when an absolute value appears in an equation, we must account for both the positive and negative value of X.

#### Section

Rules

 Examples Explanation This represents the equations x=2 and -x=2 . The solution set is {2, -2} .

The solution set of absolute value equations are often graphed on a number line. The filled circles represent the solution points (x=2, x=-2 from the previous example).

#### Linear Absolute Value Inequalities

These problems are very similar to absolute value equations. The difference is that, whereas the solution set of absolute value equations is usually a set of discrete points, the solution set of absolute value inequalities is often a range of values.

 Examples Explanation 2x+3>5 and  2x+3>-5 are the inequalities.  The solution is -4

It is important to remember to flip the greater than or lesser than sign in the case of the negative absolute value, as we did for 2X+3>-5 in this example.

Rules is equivalent to -a is equivalent to -a ≤x≤a

#### Try these exercises

Solve

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