WEBVTT
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we have to solve this inequality ex onto one minus
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X squared, cubed. It's greater than seven onto
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one minus X squared, cubed. So what I
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notice right away is that first of all, I
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need to move everything on one side. But I
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also know is that this is exactly the same terms
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. So I'm gonna bring it over X on the
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one minus X squared, cubed minus seven under one
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minus X squared. Cubed is greater than zero and
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then I'm gonna factor it age. So when there
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was a right one minus x squared cubed out here
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and then I'm gonna say what's left. So imagine
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that I remove this and remove this. I'm left
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with X minus seven is greater than zero. So
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that gives me a possible route here of X equals
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plus or minus one because one minus X squared is
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equal to zero, which means one equals X squared
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. So X equals plus or minus one. That's
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the first option where the 1st 2 options really,
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and then the other option is acceptable to seven.
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So my number line that I've produced is going to
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be have minus one on it one and then seven
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and then I'm looking at two factors. One minus
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X squared, cubed and I'm looking at X minus
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seven. And then I'm looking at the combination of
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those in Terms of them multiplied together. So I
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need something less than minus one. So what's a
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minus to plug in minus two. Here, minus
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two squared is 41 minus four is negative. Three
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and negative three cubed is negative. I don't really
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care what the number is and then minus two minus
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seven is also negative. So when I combine them
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, I get a positive. If I plug in
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zero in here, I get one cube, which
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is positive, and I get minus seven. Sorry
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, I don't need the seven part. I just
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need the negative. So that gives me a negative
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value in here between minus one and one that if
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I plug in to, um one minus two squared
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, cubed is negative again. And that's negative.
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So it gives me a positive. And then finally
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, something bigger than seven. That's a eight,
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gives me a negative and positive, which means it's
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negative. So when I look over here, I'm
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looking for where is greater than zero which means I'm
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looking for the positive places. So I'm looking for
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here and here. So my solution is going to
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be from negative infinity up to minus one. That's
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the first interval and the other interval is the interval
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from 1 to 7, and that is my answer
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.