Question

Which value of x would make FG II BC? 1 3 6 9

Answer 1

 x - 1        x + 1
------ = --------------
x + 3       x + 6

if x = 9
8/ 12 = 10/15

12 (10) = 8(15)
120 = 120

so 
answer is 9 (last choice)

Answer 2

Answer: The value of x is 9.

Explanation:

It is given that FG || BC.

If a transversal line intersect two parallel lines then the corresponding angles are same. There in triangle ACB and AGF,

$\angle GFA=\angle CBA$

$\angle AGF=\angle ACB$

Angle A is common is both triangles.

$\frac{FA}{BA}= \frac{GA}{CA}$

$\frac{x+1}{(x+1)+(x+6)}= \frac{x-1}{(x-1)+(x+3)}$

$\frac{x+1}{(2x+7}= \frac{x-1}{(2x+2)}$

$(x+1)(2x+2)=(x-1)(2x+7)$

$2x^2+4x+2=2x^2+5x-7$

$4x+2=5x-7$

$x=9$

Therefore, the value of x is 9.