Expert: Scott A Wilson - 9/23/2009

Question
So, I got the first question down. I got to this problem, and my mind literally went blank. This isn't the Geometry I learned in ninth grade. A little help, please?

Point E is a point on segment DF between points D and F. The length of segment EF is 6. What are the lengths of segments DE and DF if the length of segment DE is “5x +13” and the length of segment DF is “7x -25”?

I know that DE + EF = DF, but it's rather hard when DF is an equation.

Answer
Yes, DE + EF = DF, so just put in the values.

DE is 5x + 13, EF is 6, and DF is 7x - 25.

That gives 5x + 13 + 6 = 7x - 25.

Add 13+6 and get 19, so now the equation is 5x + 19 = 7x - 25.

Add -5x + 25 to both sides of the equation and get 44 = 2x.

Divide both sides by 2 and get 22 = x.

This means that DE is 5(22)+13 = 123 and DF is 7(22)-25 = 129.

To check, lets put these values in the equation DE + EF = DF and get 123 + 6 = 129.
Yea, that looks right to me.