Question

100 POINTS! PLEASE HELP!

1. What is the value of x? Enter your answer in the box. x = __

2. What is the value of x? Enter your answer in the box. x = __

(images below)

Answer 1

Apply angle bisector theorem

`\\ \sf\longmapsto (9)/(15)=(3)/(5)=(2x-1)/(3x)`

`\\ \sf\longmapsto 9x=5(2x-1)`

`\\ \sf\longmapsto 9x=10x-5`

`\\ \sf\longmapsto 10x-9x=5`

`\\ \sf\longmapsto x=5`

#2

`\\ \sf\longmapsto (4)/(3)=(x)/(2.25)`

`\\ \sf\longmapsto 4(2.25)=3x`

`\\ \sf\longmapsto 3x=9`

`\\ \sf\longmapsto x=3`

Answer 2

1) x = 5

2) x = 3

Explanation:

`1) \: by \: angle \: bisector \: theorem \\ (9)/(15) = (2x - 1)/(3x) \\ \\ 15(2x - 1) = 9(3x) \\ \\ 30x - 15 = 27x \\ \\ 30x - 27x = 15 \\ \\ 3x = 15 \\ \\ x = (15)/(3) \\ \\ \red{ \boxed{ \bold{ x = 5}}} \\ \\ 2) \: again \: by \: angle \: bisector \: theorem \\ (3)/(4) = (2.25)/(x) \\ \\ 3x = 4(2.25) \\ \\ 3x = 9 \\ \\ x = (9)/(3) \\ \\ \purple{ \boxed{ \bold{x = 3}}}`