Geometry Equations: finding the value of x for line segments

[Jaye]

I have a line segment and the three points on it are D (the first endpoint), E (the midpoint), and F (the last endpoint). Also:

. . .DE = x
. . .EF = 3x - 1
. . .DF = 2x + 4

I wrote the equation as:

. . .2x + 4 = x + 3x - 1

I worked it out as:

. . .2x + 4 = x + 3x - 1
. . .2x + 4 = 4x - 1
. . .4 = 2x - 1
. . .5 = 2x
. . .x = 2.5

But when I plugged in this variable, I didn't get the right answers. I would greatly appreciate anyone's help in helping get this problem right.

 

[stapel]

On what basis do you believe your answer to be incorrect?

Note: If E really is the midpoint, and not just some point between D and F, then:

. . . . .|DE| = |EF|

. . . . .x = 3x - 1

. . . . .1 = 2x

. . . . .0.5 = x

Then |DE| = 0.5 and |EF| = 3(0.5) - 1 = 1.5 - 1 = 0.5, but |DF| = 2(0.5) + 4 = 1 + 4 = 5 (instead of 0.5 + 0.5 = 1), so that won't work. Are you sure the problem specifies that E is exactly midway between D and F?

Thank you.

Eliz.

 

[Denis]

Re: Geometry Equations: finding the value of x for line segm

I have a line segment and the three points on it are D (the first endpoint), E (the midpoint), and F (the last endpoint). Also:
. . .DE = x
. . .EF = 3x - 1
. . .DF = 2x + 4
I wrote the equation as:
. . .2x + 4 = x + 3x - 1
I worked it out as:
. . .2x + 4 = x + 3x - 1
. . .2x + 4 = 4x - 1
. . .4 = 2x - 1
. . .5 = 2x
. . .x = 2.5
But when I plugged in this variable, I didn't get the right answers. I would greatly appreciate anyone's help in helping get this problem right.

E is NOT the midpoint...but is a point somewhere on DF;
with that, your solution is correct:
DE = 2.5
EF = 3*2.5 - 1 = 6.5
DF = 2.5 + 6.5 = 9
DF = 2*2.5 + 4 = 9
Why were you not getting that when you plugged ????