Question

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

Answer 1

Answer:

$x= (3, \frac{3}{10} )$

Step-by-step explanation:

The figure is composed of two similar triangles; therefore,

$\frac{7x}{19x-4} =\frac{7x+8}{(5x+5)+(19x-4)}$ 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

$x= (3, \frac{3}{10} )$