To determine the value of x in the triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the triangle has side lengths of 75, 41, and 3x + 19.
We can set up the following inequalities:
75 + 41 > 3x + 19
116 > 3x + 19 (combine like terms)
97 > 3x (subtract 19 from both sides)
32.333... > x
3x + 19 + 41 > 75
3x + 60 > 75 (combine like terms)
3x > 15 (subtract 60 from both sides)
5 > x
Therefore, x must be less than 32.333... and greater than 5.
The range of values for x is 5 < x < 32.333...
a triangle has measures 75, 41, 3x+19
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