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
