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Hey, what's up, guys? Eric? And
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today I'm gonna be walking us through how to solve
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this inequality over here graphically and AJ directly. So
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let's get started. I've graphed here absolutely, for
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close one minus three in red. And you y
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equals two in blue here with a horizontal line here
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. So, um, in our inequality were asked
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, defying the domain essentially grass if on the domain
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for X that satisfies this inequality that makes this inequality
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troop. So if we're asked when the left hand
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side is greater than the right hand side when the
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red side is greater than the right on the blue
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side were asked to find where on which vise of
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X is the red higher up than the blue.
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So you see, the two lines intersect, er
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the two grabs intersect. A X equals negative Three
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halves and X equals one. And we clearly see
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that the red is greater than the blue from negative
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infinity up to ah, negative three halves. And
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from one, all the two positive infinity. And
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I mean that means our demand of X that makes
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us about inequality is from negative infinity up to,
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but not including negative. Three halves union from one
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, not including one up to positive infinity. You
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have worked out. Ah, question directly here I've
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combined light terms and said, Isolated the absolute value
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. Set it up so that we're comparing the magnitude
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of the absolute value here. For one for X
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plus, one is greater than five and a four
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plus one is less than negative. Five. Ah
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, and those are equivalent expressions for this absolute value
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. And then I subtracting one from both sides and
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dividing four from both sides gets ourselves these two inequalities
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. X is greater than one and X is less
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than negative, perhaps. And that's the exam.
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Exact answer as what we determined. A graphically Yeah
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, that's pretty much it. Thanks for watching.