If AC = 7x-3 and CB=3x+9,then the length of AB is:
7x-3 + 3x +9
7x+3x -3 + 9 (Organizing)
10x + 6 (Adding like terms)
Since C is the middle point, the lenght of AC is equal to the lenght of CB, therefore we need to find the value of x with the following equation:
7x-3 = 3x+9
7x - 3x -3 = 9 ( Transposing 3x to the other side of the equation)
7x - 3x= 3 + 9 ( Transposing 3 to the other side of the equation)
4x = 12 (Adding like terms)
4/4x = 12/4 ( Dividing by 4 on both sides of the equation)
x= 3
Replacing 3 in 10x + 6, we have:
10*(3) + 6 = 30 + 6 = 36
Therefore the final answer is 36, option D.