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Elevation of land in the United States is given by the inequality $|h-10,019| \leq 10,301$ where $h$ is the height in feet. What is the range of elevations in the United States?

Between $-282$ and 20320

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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

00:42

Write a compound inequalit…

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The highest elevation in N…

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Elevation The highest elev…

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From a point level with an…

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The highest point in Calif…

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The elevation, or height, …

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Hey, guys. So in this problem, we're given the inequality absolute value of H minus 10,019 less than or equal to 10,003 01 And what this inequality represents is it represents the elevation of all the land, basically the range of elevation of the of all surfaces on the earth. And what the problem asked us to do is solve this inequality for more of an explicit way of, of representing this range in a compound inequality. And in order to do that, we're going to solve this inequality. So we already have our absolute value on one side of the equation all by itself. And we can split this up in tow are too many inequalities. So this is equal to H minus 10,019 is less than equal to 3 10,301 and it's also equal to H minus 10,000 and 19 greater than or equal to negative 10,003 01 Now, if you take a look at this equation right here that I just start, this is the one that we're in a solve for first. So we want to get the H by itself. So we add 10,019 to both sides of the inequality. And when we do so we're gonna get H is less than or equal to you. 20,000 20,000, 320. And now, if we take a look at this inequality right here, what we are going to get is we're going to add 10,000 and 19 to both sides and 1000 19 to both sides. And when we do, it's gonna be a TSH is greater than our equal to. So let's do some quick math right here. 10,301 minus 10,019. What's gonna happen is it will be, too. That's gonna be 98 too. So negative. 10,003 01 plus 10,019 is gonna be negative to 82. And so, if we write this as a compound inequality, the range of values of the Earth's surface basically asserts Earth's surface, its altitude is gonna arranged from negative 282 to 20,000 320. And this is our answer to this problem

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