Question

Point Q is the midpoint of GH. GQ=2X +3 and GH=5X -5. what is the length of GQ?

Answer 1

Since point Q is the midpoint of GH, GQ must be half of GH because the midpoint bisects GH. Make 2GQ = GH in an equation.

2GQ = GH ⇒ 2(2x + 3) = 5x - 5

Distribute 2 inside the parentheses.

4x + 6 = 5x - 5

Subtract 4x from both sides.

6 = x - 5

Add 5 to both sides.

11 = x

Plug 11 for x in GQ.

GQ ⇒ 2(11) + 3

22 + 3 = 25

`\boxed {GQ=25}`

Answer 2

The length of GQ is 25.

In order to find this we must first solve for x. To do that, we must note that since Q is the midpoint of GH, then GQ must be half of what GH is. So we can write this equation.

2(GQ) = GH

Now we can plug the values of those in to solve for x.

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

4x + 6 = 5x - 5

4x + 11 = 5x

11 = x

Now that we have the value of x, we can plug back into GQ and find it's length.

GQ = 2x + 3

GQ = 2(11) + 3

GQ = 22 + 3

GQ = 25