**Q: Points D, E, and F are collinear with DE < EF and DF < EF. If DE = 2x+6, DF = 3x-4, and EF = 22, what is DE?**

Answer: 14

Explanation:

First, recall that ‘DE’ refers to the length of the segment with endpoints D and E. It is the distance between D and E. Next, DON’T ASSUME that E is between the D and F! Since DE and DF are each less than EF, and all three points lie on the same line (collinear), D must be between E and F.

Draw the diagram:

__________________________

E D F

Now label the distances as they are given in the problem:

<————–22——————->

__________________________

E 2x+6 D 3x-4 F

Use the concept: Part + Part = Whole (also called the Segment Addition Postulate) to write the equation:

2x+6 + 3x-4 = 22

Solve:

5x + 2 = 22

5x = 20

x = 4

Plug x=4 back in to the ‘DE’ part:

DE = 2x+6 = 2(4) + 6 = 14.

Tip: To be sure your answer is correct, plug x=4 into the ‘DF’ part, too:

DF = 3x-4 = 3(4)-4 = 8. Now, see that the sum of the two ‘parts’ does equal the ‘whole’:

14 + 8 = 22.

Highly Effective Headline!

Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.