Question

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

Answer 1

Point Q is the midpoint of GH. That means it splits it evenly. This means GQ and QH are equal....and added together equal GH
meaning:
 2x + 3 + 2x + 3 = 5x - 5
4x + 6 = 5x - 5
6 + 5 = 5x - 4x
11 = x

so GQ and QH are : 2x + 3.....2(11) + 3....22 + 3...= 25
and GH = 5x - 5....5(11) - 5.....55 - 5    = 50 <====

Answer 2

If Q is the midpoint of GH, then the length of the measure of GQ is 25

Midpoint is the point that divides the line into two equal parts.

If Q is the midpoint of GH, then the length of the measure of GQ is 25

If Q is the midpoint of G and H, this shows that:

1. GQ = QH
2. GQ + QH = GH

Given the following measures

GQ=2x+3

GH=5x−5

Substitute equation 1 into 2 to have:

GQ + GQ = GH

2GQ = GH

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

4x + 6 = 5x - 5

Collect the like terms

4x - 5x = -5 - 6

-x = -11

x = 11

Get the length of GQ

Recall that GQ = 2x+3

Substitute the value of x into the expression to have:

GQ = 2(11) + 3

GQ = 22 + 3

GQ = 25

Hence the length of the measure of GQ is 25

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