SOLUTION: Triangles: The sum of the lengths of any two sides of a triangle must be greater than the third side. A triangle has sides as follows: the first side is 18 mm and the second side i

Question 944040: Triangles: The sum of the lengths of any two sides of a triangle must be greater than the third side. A triangle has sides as follows: the first side is 18 mm and the second side is 3 mm more than twice the third side. What are the possible lengths of the second and third sides? [hint: You will need to solve two inequalities.]
I figured out what the second and third sides have to be more than 13 mm and 5 mm, respectively. (I did this by setting the inequality to x + 2x + 3 > 18) I got the answer half correct; but I do not understand how to get the value the second and third sides have to be less than. Please help!
Answer by josgarithmetic(39630) (Show Source): You can put this solution on YOUR website!
UNDERSTANDING the triangle inequality theorem is necessary. Use it to formulate the inequalities.

Let the "third" side length be x.
The first two lengths of the triangle sides are 18 and 3+2x. Those are directly from the description.

Now, form the inequality statements using the theorem:

Simplify the system:

The first simplified inequality does not help any.
The next two are these:
, when simplified.

Solution in more condensed form, for the third side.
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