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In $15-26,$ find and graph the solution set of each inequality.$$\left|\frac{5}{2} x+2\right| \leq 0$$

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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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In $15-26,$ solve each ine…

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Solve each inequality. Giv…

all right. Hey, guys. So, Ms Problem, we're given the inequality absolute value or five have X plus two is less than zero. And right off the bat, looking at this problem, you have to You must notice that something is wrong and that something is that you're taking the absolute value of something and you're saying that that is less than zero. Whenever you take the actual value of any number, any variable, let's see a variable. Why? After value, anything is always greater than or equal to zero. Always, it's equal to zero of y zero. But any other case, absolute value of something is always greater than zero. So, in a sense, absolute value of five halves X plus two is always gonna be a positive number or zero in this case. But let's assume it's not zero. It's just a positive number, and we're saying that a positive number or a zero is basically less than zero. This is a total contradiction, does not exist, So we already know that this inequality does not make sense. And since it does not make sense, no value of axe is ever going to make this true. Basically, no X can, ah, solve this inequality. And if we really just need to graft this out, our graph of our solutions, that is just gonna be This is gonna be the real numbers. Nothing filled in. Nothing shaded in because, like I said before, no value of X is ever gonna make the absolute value of something less than zero. So thanks for listening, guys. And ah, the answer to this, by the way, just to explicitly say it out is the solution Set is empty, does not exist. Thank you for listening eyes. And I hope this helps solve this problem and understand the concept of no, um, an empty solution set when considering after value functions in.

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