Answer:
x = 3
Step-by-step explanation:
The line segment is an angle bisector thus the following ratios are equal
[tex]\frac{32}{24}[/tex] = [tex]\frac{6x+6}{9x-9}[/tex], that is
[tex]\frac{4}{3}[/tex] = [tex]\frac{6x+6}{9x-9}[/tex] ( cross- multiply )
4(9x - 9) = 3(6x + 6) ← distribute parenthesis on both sides
36x - 36 = 18x + 18 ( subtract 18x from both sides )
18x - 36 = 18 ( add 36 to both sides )
18x = 54 ( divide both sides by 18 )
x = 3
