Answer:
A) x-1 < n < 3x+5
Step-by-step explanation:
The value of n can range between the sum and difference of the lengths of the other two sides. The sum is ...
(2x +2) +(x +3) = 3x +5
The difference is ...
(2x +2) -(x +3) = x -1
For the purpose of choosing one of these answers, we must assume that the sum is greater than the difference and the value of x is such that x-1 > 0. Using these assumptions, possible values of n are ...
x -1 < n < 3x +5 . . . . . for x > 1
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Alternate Solution
The expressions for the given side lengths are both positive when x > -1. In the range -1 < x < 1, we have the condition that 2x+2 ranges from 0 to 4 and x+3 ranges from 2 to 4. That is (x+3) > (2x+2) and possible values of n are ...
lowest: (x+3) -(2x +2) = 1 -x
highest: (x+3) +(2x +2) = 3x +5
So, another possible solution is ...
1-x < n < 3x +5 . . . . . . . for -1 < x < 1
