Question

Q is the midpoint of GH¯¯¯¯¯¯ , GQ=2x+3, and GH=5x−5 .

What is the length of GQ¯¯¯¯¯ ?



Enter your answer in the box.

I know the answer is 25 but why and how?

Answer 1

It'd be best to draw it out to understand....

Answer 2

We see that we know of the equation to equal the entire length and we know GQ which is half of the length is 2x + 3 so in order to find GQ we would need to find the equation of GH....So we would subtract 5x - 5 and 2x + 3....

\(\Huge{(5x-5)-(2x+3)=GQ}\)

So what would that simplify to?

Answer 3

x=8/3

Answer 4

O_O

Answer 5

So so sorry my internet is bad...I meant we need to find QH in which the equation above is to find QH

Answer 6

So...

\(\huge{(5x-5)-(2x+3)=QH}\)

We first combine like terms to solve...

\(\huge{3x-8=QH}\)

So we know for a fact that QH and GQ have equal lengths in which we can use to find x....

\(\huge{3x-8=2x+3}\)

What would this simplify to?

Answer 7

ashley

Answer 8

x=11

Answer 9

Then it both sides equals to 25

Answer 10

\(\huge{\checkmark}\)

Answer 11

Nicely done!

Answer 12

Thank you for your help!

Answer 13

np :) sorry for long and slow replies my internet is bad

Answer 14

It's okay :)