Question

Point E is on line segment DF. Given DE = 2x, EF = 2x – 6, and
DF = 3x + 5, determine the numerical length of EF.

Answer: EF =

Answer 1

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:

$DF=DE+EF$

We are given that DE is 2x, EF is 2x-6, and DF is 3x+5. So, substitute:

$(3x+5)=(2x)+(2x-6)$

Now, solve for x.

On the right, combine like terms:

$3x+5=4x-6$

Subtract 4x from both sides:

$-x+5=-6$

Subtract 5 from both sides:

$-x=-11$

Divide both sides by -1:

$x=11$

Now that we know x is 11, substitute this back into the equation for EF to find EF.

$EF=2x-6$

Substitute 11 for x:

$EF=2(11)-6$

Multiply:

$EF=22-6$

Subtract:

$EF=16$

And we're done!