Answer:
x = 8
Step-by-step explanation:
The line segment inside the triangle is an angle bisector and divides the opposite side into segments that are proportional to the other 2 sides, that is
[tex]\frac{11x-4}{9x}[/tex] = [tex]\frac{7x}{6x}[/tex] ( cross- multiply )
6x(11x - 4) = 63x² ← distribute left side
66x² - 24x = 63x² ( subtract 63x² from both sides )
3x² - 24x = 0 ← factor out 3x from each term on the left side
3x(x - 8) = 0
Equate each factor to zero and solve for x
3x = 0 ⇒ x = 0
x - 8 = 0 ⇒ x = 8
But x > 0 , then x = 8
