Answer:
EF is 16.
Step-by-step explanation:
So we know that Point E is somewhere on Line DF. In other words, DE plus EF must equal DF. In an equation, this is:
[tex]DF=DE+EF[/tex]
We are given that DE is 2x, EF is 2x-6, and DF is 3x+5. So, substitute:
[tex](3x+5)=(2x)+(2x-6)[/tex]
Now, solve for x.
On the right, combine like terms:
[tex]3x+5=4x-6[/tex]
Subtract 4x from both sides:
[tex]-x+5=-6[/tex]
Subtract 5 from both sides:
[tex]-x=-11[/tex]
Divide both sides by -1:
[tex]x=11[/tex]
Now that we know x is 11, substitute this back into the equation for EF to find EF.
[tex]EF=2x-6[/tex]
Substitute 11 for x:
[tex]EF=2(11)-6[/tex]
Multiply:
[tex]EF=22-6[/tex]
Subtract:
[tex]EF=16[/tex]
And we're done!
