5. Point D lies between Points E and F. If ED= 4x-2, DF= 5x-7, and EF= 6x+18, find x, then find the length of ED, DF, and EF.

Step-by-step explanation:

D lies between E and F.

Length of ED + Length DF = Length of EF

       4x -2 + 5x - 7 = 6x + 18         {combine like terms}

       4x + 5x - 2 - 7 = 6x +18

                 9x - 9    = 6x + 18         {Subtract 6x form both sides}

               9x - 9 - 6x = 18

                        3x -9 = 18          {Add 9 to both sides}

                              3x = 18 + 9

                              3x = 27          {divide both sides by 3}

                                x = 27/3

x = 9

ED = 4x - 2 = 4*9 - 2 =36 - 2 = 34

DF = 5x - 7 = 5*9 - 7 = 45 - 7 = 38

EF = 6x + 18 = 6*9 + 18 = 54 + 18 = 72        

(x, y)→(x − 8, y − 7)

step-by-step explanation:

enjoy!