If a 16 foot piece of string is cut into 2 pieces so that the longer piece is 1 foot longer that twice the shorter piece if the shorter piece is x foot long, find the length of both pieces

Well,

We can write everything down based on x.

Longer piece = 2x + 1
Longer piece + Shorter piece = 16
x + 2x + 1 = 16

Collect Like Terms
3x + 1 = 16

Subtract 1 from both sides
3x = 15

Divide both sides by 3
x = 5

Longer piece = 2x + 1
Longer piece = 2(5) + 1
Longer piece = 10 + 1
Longer piece = 11

11 + 5 = 16

Longer piece = 11 ft.
Shorter piece = 5 ft.