Solving Absolute Value Inequalities

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Solve absolute value inequalities by solving the equations first, graphing the different points on an axis and shading between the different points. Learn more about absolute value, which is the positive number for any integer, with information from a tutor in this free video on math.

Part of the Video Series: Math Lessons
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Video Transcript

Hi, my name is Samir Malik. I'm a private tutor for middle school and high school students in Austin, Texas. Today we're going to solve absolute value inequalities. And I'll also, I will also show this to you by graphing. Absolute value of any number is a positive number for that number. So for example if you have the absolute value of 5, you would get 5. The absolute value for -5 would equal 5; the absolute value for -100 would equal 100 and the absolute value for 2 for example would be 2. So now we're going to graph these absolute value inequality so you have a better understanding of how it all works. We have an absolute value of say 1x 2 and is greater than 5. And we need to graph this because this is an absolute value which, absolute value equation or inequality which we need to graph. So first of all, we need to solve it so that way x 2 =5 so we know x has to equal 3. So if x is greater than 3, the equation is 2. Now we need to solve it so that x 2 = -5; that makes x equal -7. So if x is less than -7, then we have the inequality to be true as well. And then we need to graph this inequality and we can go ahead and graph this on a number line where we have the points x=3; so 0, 1, 2, 3. We'll go ahead and make that or like this and then shade it, going this way 'cause it has to be greater than 3. And then we have -7; so -1, -2, -3, -4, -5, -6, -7 is right here; we'll draw a circle on that and we'll move in this direction here. So we were able to see here that in this equation, linear equation, we have x to be greater than 3 and x has to be less than -7 for this absolute value inequality to be true. So here we're able to understand how to solve for absolute value inequalities, plus I have been able to demonstrate this to you by illustrating it on a graph and solving a, an example of absolute value inequality.

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