Question

A 14​-foot piece of string is cut into two pieces so that the longer piece is 2 feet longer than twice the shorter piece. If the shorter piece is x feet​ long, find the lengths of both pieces.

Answer 1

We are given that the shorter piece is x
From your description, the longer piece is 2x + 2
The total length is
x + 2x + 2 = 14
ie
3x + 2 = 14
3x = 12
x = 4

So the length of the shorter piece is 4 ft
Therefore the length of the longer piece must be
(14 - 4) ft = 10 ft

Answer 2

X = shorter piece
y = longer piece

x + y = 14
y = 2x + 2

x + (2x + 2) = 14
3x + 2 = 14
3x = 14 - 2
3x = 12
x = 12/3
x = 4.......shorter piece (x) is 4 ft

y = 2x + 2
y = 2(4) + 2
y = 8 + 2
y = 10...longer piece (y) is 10 ft