Answer: The value of x must be greater than 3
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Explanation:
The triangle inequality theorem will come into play here. The basic idea of this theorem is "take any two sides of a triangle and add them up. That sum must be larger than the third side".
So if we have
a = 12
b = x
c = 15
then the following must hold true (all three inequalities must be true)
a+b > c
a+c > b
b+c > a
Focus on the first inequality and plug in the given values. Then solve for x
a+b > c
12+x > 15
12+x-12 > 15-12
x > 3
So we see that x > 3. Repeat the same for the second inequality
a+c > b
12+15 > x
27 > x
x < 27
Repeat again for the third inequality
b+c > a
x+15 > 12
x+15-15 > 12-15
x > -3
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In summary so far, we have
x > 3
x < 27
x > -3
Combine all of those inequalities to form one single compound inequality which is 3 < x < 27
For some reason your teacher doesn't want you to focus on the "less than 27" part, so it seems like s/he only wants the "x > 3" portion.
So this is why x must be larger than 3 (up only til you get to 27 though).
