SOLUTION: How can I find the possible values of the perimeter of the rectangle shown? The length is 2x+4 and the width is 5-x. The answer in the book is 14<P<28 but I don't know how to get

Question 486158: How can I find the possible values of the perimeter of the rectangle shown? The length is 2x+4 and the width is 5-x. The answer in the book is 14
Answer by chessace(471) (Show Source): You can put this solution on YOUR website!
P = 2 * (L + W)
= 2 (2x+4 + 5-x)
= 2(x+9)
P = 2x + 18
Now both measurements must be > 0.
L = 2x+4 > 0 means 2x > -4, or x > -2.
W = 5-x > 0 means -x > -5 or x < 5.
Therefore -2 < x < 5 are the only possible values for x.
P(x=-2) = 14
P(x=5) = 28
Note that P(x) is linear so there is nothing weird in the mid range.
Therfore in the (only possible) range -2 < x < 5, 14 < P < 28.

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