What inequality represents possible values for the length of the third side of a triangle with side lengths of 3 inches, 7 inches, and c inches?

To find the possible values for ( c ), we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Given the side lengths 3 inches, 7 inches, and ( c ) inches, we can set up the following inequalities:

1. ( 3 + 7 > c ) → ( c < 10 ) 2. ( 3 + c > 7 ) → ( c > 4 )
3. ( 7 + c > 3 ) → ( c > -4 ) (This inequality is always true since ( c ) must be positive.)

So the relevant inequalities for ( c ) are ( c < 10 ) and ( c > 4 ).

Putting this together, the possible values for ( c ) can be described by the inequality:

[ 4 < c < 10 ]

This means ( c ) must be more than 4 inches and less than 10 inches. If you have any more questions or need further clarification, feel free to ask!