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Let x = shorter piece.
x + 7x = 32
x + 7x = 32
x=8
According to the problem, the total length of the rope is 32 ft. So, we can write the equation:
x + 7x = 32
Combining like terms:
8x = 32
To solve for x, we divide both sides of the equation by 8:
x = 32/8
x = 4 ft
Therefore, the length of the shorter piece is 4 ft.