The perimeter of a triangle is 84m. the longest side of the triangle is 7m less than twice the length of the shortest side, x. the middle side is 7m longer than the shortest side. what is the length of each side of the triangle.

Side1 + side2 + side 3 = 84

side1 is the shortest side, and its length is x.
side2 is the middle side, and its length is x + 7
side3 is the longest side, and its length is 2x - 7

x + x + 7 + 2x - 7 = 84

4x = 84

x = 21

side1 = x = 21
side2 = x + 7 = 21 + 7 = 28
side3 = 2x - 7 = 2(21) - 7 = 42 - 7 = 35

The length of the sides are 21 m, 28 m, and 35 m.

Looks pretty good to me!