Solving Absolute Value Inequalities

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In this section, we will learn how to solve absolute value inequalities. This means we will once again focus on the concept of absolute value. The absolute value of a number is the distance between that number and zero on the number line. Here instead of thinking about absolute value equations, we will discuss the concept of an absolute value inequality. Think for a minute about what the following means: |x| > 3. Again, we need to revisit the concept of absolute value for this to make sense. We are saying x can be any value whose absolute value or distance from zero is larger than 3. This means x can be any value larger than +3, or less than -3. In interval notation, we can show the solution set as: (-∞,-3) ∪ (3,∞). We also will encounter problems in which we reverse the symbol. Suppose we see |x| < 3. Now we are asking for values where the absolute value or distance from zero is less than 3. This would be all numbers between -3 and 3, or (-3,3) in interval notation.
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