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


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


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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}


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