WEBVTT
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this problem forty one of this tour calculus In addition
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, section two point four How close to negative three
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Do we have to take X so that one divided
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by the quantity X plus three to the fourth power
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is greater than ten thousand? First we'Ll solve this
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algebraic lee we'LL divide by ten thousand on about science
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while also multiplying by the quantity Extra story to thie
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fourth power They won't take the forth route on both
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sides Here we'LL have X plus three that quantity to
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the fourth to the one fourth power Right, So
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we're doing one fourth power to vote science so that
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we can cancel out forthe here on the left We
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should be really able to reduce system into one tent
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because ten to the fourth power is ten thousand on
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the red side. We want to assure that this
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quantity as illustrious positive So we write it as the
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absolute value of X mystery. This specifically is the
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distance between value's X and negative three. And when
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we see that it must be values Liston one ten
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toe or point one And so that's how close we
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have to be and we can also do this graphically
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. Take this function one over the quantity X plus
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three to the fourth power and plotted against ten thousand
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to see where this across the function. And we
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see in this case that our heartbreak solution is correct
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within a point one anything less guarantees a value greater
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than ten thousand on exactly as zero point one is
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where I won't get the exact value of ten thousand
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. So the answer is that we have to be
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closer than zero point one in order for the statement
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to be true.