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Okay next time for shoppers What is the range of

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all possible values of x for angle df if d

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is to explain a seven e f is three x

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plus nine and gf is two x plus five Okay

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interesting problem here Three lines have met forming a triangle

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and psych test takers everywhere are scrambling to determine a

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little fact about this unholy union Like all heroes intent

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on saving the universe from evil we need a strategy

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Our strategy relies on the triangle inequality serum It says

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that some of the lengths of any two sides of

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a triangle must be greater than the length of the

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third side Right Otherwise the triangle wouldn't touch so with

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angle df we know that d plus e s greater

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than d f e f plus d f is greater

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than d e n d f plus d e is

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greater than e f right So all the little side

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thing he's touch will use this knowledge along with the

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more algebraic definitions of the seides find all the possible

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ranges of x let's start with d plus c f

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his great of ndf and we'll get to x minus

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seven plus three X plus nine is greater than two

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x plus five But when we solve this inequality we

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end up with yes x is greater than one right

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Actually did all the math get point that x is

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greater Next we have df plus cf scarier than d

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e that gives us two x plus five plus two

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extra stein's greater than to explain it's Seven solve it

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and we get axes while greater than what is that

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negative seven Yeah well this is obvious because we already

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know that x is greater than once Of course it

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has to be great the negative seven as well We

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can't have a triangle with negative sides at least not

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in this reality So lastly let's solve df plus de

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is greater than e f and we get two x

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plus five plus two extra money Seven is greater than

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three x plus nine This will give us access great

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event while eleven This inequality trumps the other two and

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is the only one that matters and the value of

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x can be anything It wants to be as long

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as it's larger than eleven So the answer is d 00:01:57.456 --> [endTime] and yes we are shmoop oh snap

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