How do you solve and write the following in interval notation: #( 2 x  1 ) / ( x  3 ) <1#?
Cross multiply and reverse the inequality.
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To solve the inequality ( \frac{2x  1}{x  3} < 1 ) and write it in interval notation, you first find the critical points by setting the inequality equal to 1 and solving for x. Then, you test the intervals between these critical points to determine where the inequality holds true.

Set ( \frac{2x  1}{x  3} = 1 ) and solve for x: [ 2x  1 = x  3 ] [ x = 2 ]

Test the intervals: a) Test the interval (∞, 2): Choose a test point, for example, x = 3: ( \frac{2(3)  1}{3  3} = \frac{7}{6} > 1 ) The inequality does not hold in this interval.
b) Test the interval (2, 3): Choose a test point, for example, x = 0: ( \frac{2(0)  1}{0  3} = \frac{1}{3} < 1 ) The inequality holds in this interval.
c) Test the interval (3, ∞): Choose a test point, for example, x = 4: ( \frac{2(4)  1}{4  3} = \frac{7}{1} > 1 ) The inequality does not hold in this interval.
Therefore, the solution to the inequality ( \frac{2x  1}{x  3} < 1 ) in interval notation is (2, 3).
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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