How do you solve and graph the compound inequality 4 < n + 6 < 9 ?

1 Answer
Somebody N.
Mar 22, 2018

See below.

Explanation:

4 < n+6 < 9

Subtract 6 from each part of the inequality:

4 -6< n+6-6 < 9-6

color(blue)(-2 < n < 3)

To graph:

Make two equations:

We have:

n> -2 , n+2>0

Equation y=n+2

n < 3 , n-3 < 0

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 <= , >=, so the line will not be an included region.

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.

enter image source here

Region A:

coordinates:

(-3,2)

n+2 > y

(-3)+2 > 2 \ \ \ \ \ \ \ \ False

n-3 < y

(-3)-3 < 2 \ \ \ \ \ \ \ \ True

Region B:

coordinates:

(2,2)

n+2 > y

(2)+2 > 2 \ \ \ \ \ \ \ \ True

n-3 < y

(2)-3 < 2 \ \ \ \ \ \ \ \ True

Region C

coordinates:

(-2,4)

n+2 > y

(-2)+2 > 2 \ \ \ \ \ \ \ \ False

n-3 < y

(4)-3 < 2 \ \ \ \ \ \ \ \ \ \ \ \ \ True

The only region where both conditions are met is region B. Shade region B

enter image source here

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