SOLUTION: We are learning about The Triangle Inequality and I am stuck on a question: If the sides of a triangle have the following lengths, find all possible values of x. AB=2x+5, BC=3x-2

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Question 390952: We are learning about The Triangle Inequality and I am stuck on a question:
If the sides of a triangle have the following lengths, find all possible values of x.
AB=2x+5, BC=3x-2, AC=4x-8
(The answer the book has is X > 3, but I am not sure how)
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: A triangle with sides 'a', 'b', and 'c' is only possible if a%2Bb%3Ec. Note: the labels are arbitrary which means that the labels can be rearranged. For example, we can also say a%2Bc%3Eb or b%2Bc%3Ea. The basic idea is that the sum of any two sides must be greater than the remaining third side.


So this means that you have these 3 inequalities


AB%2BBC%3EAC

AB%2BAC%3EBC

BC%2BAC%3EAB


Make the proper substitutions and solve for x in each inequality. Once you have the 3 solution sets, find the intersection of the 3 sets to find your answer.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim