How do you solve and graph the compound inequality #4 < n + 6 < 9# ?
See below.
Subtract 6 from each part of the inequality:
To graph:
Make two equations:
We have:
Equation
Graph these two lines. This we give you the boundary between included and excluded regions. Remember to use a dotted line as these are of the for < , > and not of the form
With these plotted, we have three regions A , B and C, we now test coordinates in each region to see which is an included or excluded region.
Region A:
coordinates:
Region B:
coordinates:
Region C
coordinates:
The only region where both conditions are met is region B. Shade region B
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To solve and graph the compound inequality (4 < n + 6 < 9):

Subtract 6 from all parts of the compound inequality: (4  6 < n + 6  6 < 9  6) (2 < n < 3)

Plot an open circle at 2 and 3 on a number line, as they are not included in the solution set.

Shade the region between 2 and 3, indicating all values of (n) that satisfy the compound inequality.
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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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