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c must be less than 10 but greater than 4.

Step-by-step explanation:

In order to solve this problem, you have to apply the triangle inequality theorem. This theorem is used to determine whether or not you can form a triangle. According to the theorem, the sum of the two sides must be greater than the longest side of the triangle.

For instance, a triangle has side lengths 4, 5, and 7.

Can you form a triangle with these values?

Well, let's see

Since 4 and 5 are values less than 7, you are going to be adding those numbers. 4 plus 5 is 9. 9 is greater than 7. This means that you can form a triangle with those numbers.

For this question, you are given a triangle that has the side lengths of 3 inches, 7 inches, and c inches. The question wants the range of values. Make c the shortest side and the longest side.

Let's start with longest first.

take 3 and 7

Add them and you will get 10.

10 is greater than c. or c<10.

For the shortest side make 7 the longest

3 plus c is less than 7

subtract 3 from both sides

then you get c is less than 4. or c<4.

So you have c<4 and c>10.

combine them to make a long inequality.

4<c<10.

That is your answer.

36

step-by-step explanation: