Answer:
x = 40/7
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}=\dfrac{10-x}{6}[/tex] cross multiply
[tex]6x=8(10-x)[/tex] use distributive property
[tex]6x=(8)(10)+(8)(-x)[/tex]
[tex]6x=80-8x[/tex] add 8x to both sides
[tex]14x=80[/tex] divide both sides by 14
[tex]x=\dfrac{80}{14}[/tex]
[tex]\boxed{x=\dfrac{40}{7}}[/tex]
