Answer: We know that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using the triangle inequality theorem, we can set up the following inequality:
BD + BC > CD
7x - 10 + 4x - 29 > 5x - 9
Simplifying, we get:
11x - 39 > 5x - 9
Subtracting 5x from both sides, we get:
6x - 39 > -9
Adding 39 to both sides, we get:
6x > 30
Dividing by 6 from both sides, we get:
x > 5
So x must be greater than 5.
To find the value of BD, we can substitute the value of x in the equation:
BD = 7x - 10
BD = 7(5) - 10 = 25 - 10 = 15
To find the value of BC, we can substitute the value of x in the equation:
BC = 4x - 29
BC = 4(5) - 29 = 20 - 29 = -9
To find the value of CD, we can substitute the value of x in the equation:
CD = 5x - 9
CD = 5(5) - 9 = 25 - 9 = 16
So, BD = 15, BC = -9, CD = 16
Explanation: