Answer:
x = 27
Step-by-step explanation:
Look at the picture.
If ABC is any triangle and AD bisects (cuts in half) the angle BAC, then
[tex]\dfrac{AB}{BD}=\dfrac{AC}{DC}[/tex]
In our triangle we have the proportion:
[tex]\dfrac{x+8}{10}=\dfrac{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[/tex]
