Solving Combined Inequalities

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Solving combined inequalities requires taking two inequalities with variables in them and solving the equations accordingly to calculate the appropriate variable. Find the value of a variable that fits both inequalities with help from a tutor in this free video on math.

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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 the Austin, Texas area. Today I'm going to be discussing how to solve combine inequalities. Now the way to solve combine inequalities is you take two inequalities with variables in them and you solve them accordingly to solve for the appropriate variable. So I like to show this to you by illustrating this with an example as well. We're going to go ahead and solve for this so we know that in this equation 3x-2 has to be greater than -8, which means that 3x has to be greater than -6, which means x has to be greater than -2 for this part to be true for this first half portion. Now for the second half portion we have 3x-2 is less than 13, so we have 3x has to be less than 15, which means x has to be less than 15/3, which means x has to be less than 5. So if we know from this inequality that x has to be greater than -2 or can be greater than -2 for any, for this to be true and if it's greater than -2, this equation will be true; but at the same time x has to be less than 5 for this equation to be true as well. So x has to fit both requirements of being greater than -2 and less than 5. So we can go ahead and write x has to be greater than -2 and x has to be less than 5 when writing the solutions up for this inequality. So here I've gone ahead and shown you the way to describe combining two inequalities together.

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