What are absolute value inequalities and regular inequalities?

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What are absolute value inequalities and regular inequalities?

Oct 29th, 2015

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The absolute value of a number measures its distance to origin on real number line.

Since 5 is at 5 units distance from origin 0, absolute value of 5 is 5,=5.

Same properties of Inequality apply when solving an absolute value inequality as when solving a regular inequality. Main difference is that in absolute value inequality, one needs to evaluate inequality twice to account for both positive and negative possibilities for the variable.

Example: 3|h| < 21. First step is to isolate the absolute value term on one side of the inequality. One can do that by dividing both sides by 3, just as one would do in a regular inequality. With inequality in simpler form, one can evaluate absolute value as h < 7 and h > -7. The range of possible solutions for the inequality 3|h| < 21 is all numbers from -7 to 7 (not including -7 and 7).


Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 29th, 2015

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