Absolute Value Inequalities Here are the steps to follow when solving absolute value inequalities:
(quantity inside absolute value) < -(number on other side) The same setup is used for a ³ sign. If your absolute value is less than a number, then set up a three-part compound inequality that looks like this: -(number on other side) < (quantity inside absolute value) < (number on other side) The same setup is used for a £ sign This process can be a little confusing at first, so be patient while learning how to do these problems. Let�s look at some examples. Example 1: |x + 4| - 6 < 9
Example 2: |2x � 1| - 7 ³ -3
Example 3: |5x + 6| + 4 < 1
Example 4: |3x � 4| + 9 > 5
Can you take absolute value of both sides of an equation?Explanation: When we have absolute values on both sides of the equations, we must consider both possibilities for acceptable solutions - positive and negative absolute value expressions. Both sides of the equation contain absolute values.
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