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How to Solve Absolute Value Inequalities By Elise Hansen; Updated May 18, Solving absolute value inequalities is a lot like solving absolute value equations, but there are a couple of extra details to keep in mind. Definition of Absolute Value Inequality First of all, an absolute value inequality is an inequality that involves an absolute value expression.
Sciencing Video Vault How to Solve an Absolute Value Inequality The steps to solving an absolute value inequality are much like the steps to solving an absolute value equation: Isolate the absolute value expression on one side of the inequality. Solve the positive "version" of the inequality.
Solve the inequality for x: All you have to do is add 3 to each side: Now there are two "versions" of the inequality that we need to solve: This is a simple inequality; you just have to solve for x as usual.
Subtract 5 from both sides, then divide both sides by 5. Solve the Negative "Version" of the Inequality To understand this next bit, it helps to remember what absolute value means. Now back to the problem above.
Now, any positive number bigger than five is going to be further away from zero than five is. Now think a little further. What else is five units away from zero? Well, negative five is. And anything further along the number line from negative five is going to be even further away from zero.
Check yourself by plugging in a few possible solutions to make sure the inequality still holds true. Absolute Value Inequalities With No Solution There is a scenario where there would be no solutions to an absolute value inequality.
Interval Notation To write the solution to our main example in interval notation, think about how the solution looks on the number line. These solutions point away from each other, not toward each other, so take each piece separately.Sep 03, · on a slow weekday, you spend at least 2 hours on homework.
on a busy weekday, you spend up to 5 hours. write an absolute value inequality that represents the # of hours you spend on HW on a typical schwenkreis.com: Open.
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Learn to solve word problems that ask us to apply our new absolute value knowledge. Learn to solve word problems that ask us to apply our new absolute value knowledge.
Absolute value word problems. About Transcript. Learn to solve word problems that ask us to apply our new absolute value knowledge.
This tutorial shows you how to translate a word problem to an absolute value inequality. Then see how to solve for the answer, write it in set builder notation, and graph it on a .
These absolute value word problems in this lesson will explore real life situations that can be modeled by either an absolute value equation or an absolute value inequality. Write an absolute value inequality that model your weight loss.
Jul 14, · Absolute Value Word Problem Christina Jeffreys. Absolute Value Inequality Word Problems - Duration: Writing an Absolute Value Inequality from a Graph - Duration.