Segments bc and de are parallel. find x
a. 5
b. 4
c. 6
d. 7

C. 6  

Step-by-step explanation:

∆ABC and ∆ADE are similar triangles.

                       AB/AC = AD/AE

(x - 1 + x + 2)/(15 + 24) = (x - 1)/15

                 (2x + 1)/39 = (x - 1)/15         Multiply each side by 39

                        2x + 1 = 39(x - 1)/15     Multiply each side by 15

                   15(2x + 1) = 39(x - 1)         Distribute 15 and 39

                    30x + 15 = 39x - 39        Add 39 to each side

                   30x + 54 = 39x               Subtract 30x from each side

                              54 = 9x                Divide each side by 9

                                x = 6

Check:

(6 - 1 + 6 + 2)/(15 + 24) = (6 - 1)/15

                          13/39 = 5/15

                                ⅓ = ⅓