If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?

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If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?

By segment addition, we know that:
EF + FG = EG

Substituting in our values for the 3 segments, we get:
9x - 17 + 17x - 14 = 20x + 17

Group like terms and simplify:
(9 + 17)x + (-17 - 14) = 20x - 17
26x - 31 = 20x - 17

Solve for x in the equation 26x - 31 = 20x - 17

Step 1: Group variables:
We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides
26x - 31 - 20x = 20x - 17 - 20x

Step 2: Cancel 20x on the right side:
6x - 31 = -17

Step 3: Group constants:
We need to group our constants -31 and -17. To do that, we add 31 to both sides
6x - 31 + 31 = -17 + 31

Step 4: Cancel 31 on the left side:
6x = 14

Step 5: Divide each side of the equation by 6
6x/6 = 14/6
x = 2.3333333333333