Answer:
Step-by-step explanation:
Set this up according to the Triangle Proportionality Theorem:
[tex]\frac{3x}{4x}=\frac{3x+7}{5x-8}[/tex]
Cross multiply to get
[tex]3x(5x-8)=4x(3x+7)[/tex]
and simplify to get
[tex]15x^2-24x=12x^2+28x[/tex]
Get everything on one side of the equals sign and solve for x:
[tex]3x^2-52x=0[/tex] and
[tex]x(3x-52)=0[/tex]
By the Zero Product Property,
x = 0 or 3x - 52 = 0 so x = 17 1/3
