Question

O is the midpoint of segment FG. FO=3x+17, OG=7x-15. 98 points

Answer 1

Hey!

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Find the value of x:

OG and FO need to be equal first.

~Create an inequality

7x - 15 = 3x + 17

~Subtract 3x to both sides

7x - 15 - 3x = 3x + 17 - 3x

~Simplify

4x - 15 = 17

~Add 15 to both sides

4x - 15 + 15 = 17 + 15

~Simplify

4x = 32

~Divide 4 to both sides

4x/4 = 32/4

~Simplify

x = 8

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Substitute for the inequality:

7x - 15 = 3x + 17

7(8) - 15 = 3(8) + 17

56 - 15 = 24 + 17

41 = 41

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Add together:

41 + 41 = 82

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Answer:

$\large\boxed{Midpoint~is~42~units!}$

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Hope This Helped! Good Luck!

Answer 2

O is the midpoint so both sides FO and OG need to equal each other.

3x + 17 = 7x - 15

Subtract 3x from both sides:

17 = 4x -15

Add 15 to both sides:

32 = 4x

Divide both sides by 4:

x = 32/4

X = 8

Now you have the value of X, solve for the lengths:

FO = 3x +17 = 3(8) +17 = 24 +17 = 41

OG = 7x -15 = 7(8) -15 = 56-15 = 41

Total length would be 41 + 41 = 82