Question

Please help me with the question. You must solve for x.

Answer 1

`x= (3, (3)/(10) )`

Explanation:

The figure is composed of two similar triangles; therefore,

`(7x)/(19x-4) =(7x+8)/((5x+5)+(19x-4))` this says the ratio of the sides is same for the two triangles.

we simplify and a rearrange to get

`7x(24x+1)=(7x+8)(19x-4)`

which we expand and get

`168x^2+7x=133x^2+124x-32`

`35x^2-117x+32=0`

this quadratic equation has solutions

`x=3.04`

`x=0.30`

As integers and simplified fractions these are

`x= (3, (3)/(10) )`