Question

What is the value of x?

Answer 1

Explanation:

Set this up according to the Triangle Proportionality Theorem:

`(3x)/(4x)=(3x+7)/(5x-8)`

Cross multiply to get

`3x(5x-8)=4x(3x+7)`

and simplify to get

`15x^2-24x=12x^2+28x`

Get everything on one side of the equals sign and solve for x:

`3x^2-52x=0` and

`x(3x-52)=0`

By the Zero Product Property,

x = 0 or 3x - 52 = 0 so x = 17 1/3