Final answer:
To find the lengths of two pieces of a board where one piece is 7 inches shorter than the full 65-inch board, we calculate the shorter piece as 65 inches minus 7 inches, which equals 58 inches. The longer piece remains 65 inches.
Step-by-step explanation:
The question requires us to find the length of two pieces of a board when one piece is known to be 7 inches shorter than the full length of 65 inches. The length of the longer piece is 65 inches by definition. To find the length of the shorter piece, we subtract 7 inches from the full length:
Simplifying the equation, we get 2x - 7 = 65. Adding 7 to both sides, we have 2x = 72. Dividing both sides by 2, we get x = 36. Therefore, the length of the board is 36 inches and the length of the shorter piece is 36 - 7 = 29 inches.
Length of shorter piece = 65 inches - 7 inches = 58 inches.
Now we have the lengths of both pieces: the longer piece is 65 inches, and the shorter piece is 58 inches.