Final answer:
To find the lengths of two ribbon pieces where one is 3 inches longer than the other, we set up the equation 2x + 3 = 14, leading us to conclude the shorter piece is 5.5 inches and the longer piece is 8.5 inches.
Step-by-step explanation:
The student's question involves setting up and solving an algebraic equation to find the lengths of two pieces of ribbon when one is known to be longer than the other. The ribbon has a total length of 14 inches, and we let x represent the length of the shorter piece. The longer piece, therefore, would be x + 3 inches. To find the value of x, we must set up an equation accounting for the total length of the ribbon:
x + (x + 3) = 14
Combining like terms gives us:
2x + 3 = 14
Subtracting 3 inches from both sides we get:
2x = 11
Dividing both sides by 2 gives us:
x = 5.5.
This means the shorter ribbon is 5.5 inches long and the longer ribbon is 8.5 inches long (since 5.5 + 3 = 8.5).