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In $15-26,$ find and graph the solution set of each inequality.$$2|x+2| \leq-3$$

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Chapter 3

REAL NUMBERS AND RADICALS

Section 1

The Real Numbers and Absolute Value

Whole which of Numbers

Fractions and Mixed Numbers

Decimals

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In $15-26,$ find and graph…

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Solve each inequality. Gra…

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In $15-26,$ solve each ine…

all right. Hey, guys. So in this problem were given two times absolute value of experts to is less than or equal to minus the reef. And so first, before we even try to simplify this inequality, let's just take a look at it and see if it actually makes sense when you take the absolute value of anything, right, And after the value of any know. So let's just say absolute value of some blah something right here. You're going to get the positive value. You're absolutely you of anything is always going to give you something greater than or equal to 00 everything abso value of zero. But any number of plug it in, it gives you something greater than zero. So what we're saying right now is when we take our absolute value of X Plus, two were basically saying our experts to this value, whatever our absolute value of experts to is, it's gonna be greater than zero. So we know that this is gonna be greater than zero and basically were multiplying something that's greater than zero. Something that's positive by another positive number two. So we're basically essentially multiplying a positive times. A positive on the left hand side of this equation, and when you do that, you're going to get another positive number Positive times positive is always positive. But what this inequality is saying is that it's saying that positive number is less than or equal to minus three. This can never, ever happen. And when you're solving inequalities like these, it's important to check if the inequality actually makes sense that if is it, if it is even possible for the solution set to exist and one of the case, one of the best ways to check if a solution said does it does not exist is if the inequality the problem that's given itself does not make sense, like in this case. And in this case, the problem basically breaks down to saying that a positive number is less in a negative number. So in this case, there is not going to be any solution set because no value of X doesn't matter what value of X you choose in the real numbers. So basically saying no value of X in the reels will ever make this inequality true. And since this is the case, the solution set is empty, meaning it does not exist. There is no value of X that makes this solution true. And that is the answer to this quality problem. Thank you for listening, guys. And I hope this help. This was a new concept when you're solving inequalities problems. I hope this helped Segway us into this new set of problems. Thank you for listening and

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