Question

What is value of x?

Enter your answer in the box.

x =

Answer 1

x = 27

Explanation:

(x+8) / 10 = (2x - 5) / 14

Cross multiply

10(2x - 5) = 14(x + 8)

20x - 50 = 14x + 112

6x = 162

x = 27

Answer 2

x = 27

Explanation:

Look at the picture.

If ABC is any triangle and AD bisects (cuts in half) the angle BAC, then

`(AB)/(BD)=(AC)/(DC)`

In our triangle we have the proportion:

`(x+8)/(10)=(2x-5)/(14)\qquad\text{cross multiply}\\\\14(x+8)=10(2x-5)\qquad\text{use distributive property}\ a(b+c)=ab+ac\\\\(14)(x)+(14)(8)=(10)(2x)+(10)(-5)\\\\14x+112=20x-50\qquad\text{subtract 112 from both sides}\\\\14x=20x-162\qquad\text{subtract 20x from both sides}\\\\-6x=-162\qquad\text{divide both sides by (-6)}\\\\x=27`