How do you solve the inequality #x^2  9x> 18#?
The solutions are
The inequality is
Let's build a sign chart
Therefore,
graph{x^29x+18 [4.29, 15.71, 3.96, 6.04]}
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(inf., 3) and (6, +inf.)
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To solve the inequality ( x^2  9x > 18 ), you first set it equal to zero and find the critical points, then determine the intervals where the inequality holds true.
 ( x^2  9x + 18 > 0 ) (adding 18 to both sides)
 ( (x  6)(x  3) > 0 ) (factoring the quadratic expression)
The critical points are where the expression equals zero, so ( x = 6 ) and ( x = 3 ).
Now, you can create a sign chart to determine the intervals where the inequality is satisfied.

Test a value in each interval into the factored expression to see if it's positive or negative.

The intervals are ( (\infty, 3) ), ( (3, 6) ), and ( (6, \infty) ).
Testing a value in each interval:
 For ( (\infty, 3) ): Pick ( x = 0 ), ( (0  6)(0  3) > 0 ), which is true.
 For ( (3, 6) ): Pick ( x = 4 ), ( (4  6)(4  3) > 0 ), which is false.
 For ( (6, \infty) ): Pick ( x = 7 ), ( (7  6)(7  3) > 0 ), which is true.
So, the solution to the inequality is ( x \in (\infty, 3) \cup (6, \infty) ).
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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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