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>> Here are our answers. You've learned that inequalities have ranges of values
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that are solutions to them. So that means that if a number falls in this range,
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we can use it in the inequality to make a true statement. Some of these may be a
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bit confusing though. For example, 3 is less than or equal to 7. On a number
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line, if we're curious about all of the numbers that are less than or equal to
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7, we would shade in all the numbers to the left of 7 on the number line. And
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then draw a square bracket to include 7 in that range. We can see that 3
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definitely falls in this region. It is not equal to 7, but it is less than 7.
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And it only needs to fit one of the criteria implied by this symbol. It either
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needs to be less than 7, or it needs to be equal to 7. Similarly, the statement
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8 is greater than or equal to 1 plus 7 is also true. When simplified, this of
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course gives us the inequality 8 is greater than or equal to 8. And you might at
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first think, oh my gosh, 8 is not greater than 8. However it only needs to be
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greater than or equal to 8. It's equal to 8 so that's enough to satisfy this
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inequality. We can see the difference here then, between this symbol, the
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greater than or equal to, which implies inclusion of 8, versus the just greater
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than sign. This statement is true. Whereas this statement is not, because 8 is
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greater than 1 plus 7, only allows for the greater than criterion, not the equal
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to one. 1 plus 7 no longer fits the bill.