Question

Point 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.

____ units

Answer 1

The length of GQ is 25/3 units.

Step-by-step explanation:

To find the length of GQ, we need to equate GQ to GH and solve for x. Since Q is the midpoint of GH, the lengths GQ and QH are equal. Therefore, we have the equation:

2x + 3 = 5x - 5

Subtract 2x from both sides:

3 = 3x - 5

Add 5 to both sides:

8 = 3x

Divide both sides by 3:

x = 8/3

To find the length of GQ, substitute the value of x back into 2x + 3:

GQ = 2(8/3) + 3

GQ = 16/3 + 3

GQ = 16/3 + 9/3

GQ = 25/3 units

Answer 2

Since point Q is the midpoint of GH, that means that GH-GQ=HQ=GQ (since Q is the midpoint). Plugging them in, we get 5x-5-(2x+3)=3x-8=GQ=HQ. Since Q is the midpoint, that means that 3x-8=2x+3=GQ=HQ. Subtracting 2x from both sides as well as adding 8, we get that x=11 and 2(11)+3=25=GQ by plugging x into 2x+3