WEBVTT
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All right. So for this example, we're being
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asked to write the compound inequality to represent a given
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phrase. And then we're gonna graph the solution set
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on the number one. So let's take a look
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at our freeze here. Were given that all real
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numbers less than seven and greater than or equal to
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negative five. Well, the first part says we're
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talking about numbers that are less than seven. So
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how would we write in inequality for this? Well
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, we would simply have X is less than seven
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. Now, the key word here is an an
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statement, so we'll use the word. And so
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what is the second part? Say it says that
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were greater than or equal to negative five. So
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that means X could be greater than or equal to
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negative five. So this is one perfectly good way
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to write our inequality here. Now, remember,
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we could also rewrite it as just one, um
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, compound inequality without using the word. And so
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we're going to start with our smallest value, which
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is the negative five, and we're gonna flip it
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around. So in other words, I'm gonna put
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the negative five first in the X second. But
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remember, that means my inequality sign also must flip
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so it become less than or equal to. So
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now, when we write our compound inequality, we're
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gonna start with the smaller value. So we're gonna
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have negative five is less than or equal to x
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. And remember, X could be less than seven
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. So we're gonna have X is less than seven
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. So this is another way we could write the
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same compound inequality. Okay, so now the next
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thing we need to dio is graft a solution set
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. So we're going to set up our number line
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. We're gonna put our key values on here.
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We have negative five and seven and negative five.
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We're gonna have a close circle because it's less than
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or equal to X and at seven will have an
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open circle because it's strictly less than X or X
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is less than seven. So remember, kind of
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like, what are inequality shows? X is in
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between negative five and seven. So that's gonna be
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the same thing on a number line. We're going
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to shade in between negative five and seven. So
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this would be all the real numbers that are less
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than seven and at the same time are greater than
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or equal to negative five