WEBVTT
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So in this example, we're being asked to write
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the compound in the quality for the given freeze.
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Then we're going to draft the solution set on the
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number line. So the given free is that we
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have. It says that all real numbers that are
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greater than or equal to seven or less than negative
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five. So it might be helpful to start by
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graphing this on the number line in order to help
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us create our inequality. So the first thing is
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, well, what values air really important here?
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What are key values? Well, that would be
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seven and negative five. And remember, when you
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put them on the number line, the smaller of
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the two has to go on the left. So
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we have to put negative five first and then seven
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on the right, and you could put values in
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between if you'd like. That's perfectly fine. All
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right, let's start with the first part of this
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freeze. It says We're talking about all real numbers
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that are greater than or equal to seven. Well
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, does that mean sevens included? Well, it
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is because it says it could be greater than or
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equal to seven. So in terms of our number
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line, we're gonna have a close circle at seven
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. Well, where? The values that are greater
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than or equal to seven. Well, they would
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be to the right, So we're going to shade
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the right hand side of our number line. So
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any values in this red shaded area will make the
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first part of our sentence true, because all of
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these values are greater than or equal to seven.
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So now let's take a look at the second part
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of our sentence. It says that these real numbers
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could be also less than negative five. Well,
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does that mean negative? FIEs included. It's not
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strictly has to be less than negative five, Which
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means that it negative five on a number line will
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have an open circle. Now, where are values
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that are less than negative? Five? Well,
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they would be to the left. So we're on
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our number line. We're gonna shade to the left
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of negative five because any of the numbers in the
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shaded area are all values that are all real numbers
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. I should say that are less than negative five
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. So now we've graft our solution on the number
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line. Now we need to write inequality statement to
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represent this number line, which in fact, represents
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our original phrase. So let's start by writing a
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number in the inequality to represent the first half of
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our number line. Well, these values of X
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so again always start with a variable, and then
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our key numbers negative. Five. Well, remember
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these air less than negative five. So we'll have
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a less than sign on. We put the or
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equal to part because negative five is not included in
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the solution set. Now let's write inequality to represent
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the right half. So again we'll start with X
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. We know we're gonna end with our key value
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of seven, and these values are all greater than
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seven or they could be equal to it, so
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we'll use a greater than or equal to sign.
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And the Onley. Everything that you need to include
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is the word. Or so you always want to
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make sure you include that word in your, um
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, compound inequality. So now we have written our
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compound in the quality to represent the phrase X is
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less than negative. Five or X is greater than
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or equal to seven now, just so you know
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, the order that you put your two inequalities doesn't
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matter. So you could have also written this kind
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of going on in the order that your original phrase
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set you could have also written this as X is
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greater than equal to seven or X is less than
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negative five. Either way is perfectly fine.