A rectangle has length 7x+3 and width 2x-1. If its perimeter is 46, find x.

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Multiple Choice

A rectangle has length 7x+3 and width 2x-1. If its perimeter is 46, find x.

Explanation:
Perimeter of a rectangle is twice the sum of its length and width, so use P = 2(length + width). With length 7x + 3 and width 2x − 1, set 2[(7x + 3) + (2x − 1)] = 46. Combine inside: 7x + 3 + 2x − 1 = 9x + 2, so 2(9x + 2) = 46, giving 18x + 4 = 46, hence 18x = 42 and x = 42/18 = 7/3. Checking quickly: length = 7*(7/3) + 3 = 58/3, width = 2*(7/3) − 1 = 11/3, sum = 69/3 = 23, and 2×23 = 46, which matches.

Perimeter of a rectangle is twice the sum of its length and width, so use P = 2(length + width). With length 7x + 3 and width 2x − 1, set 2[(7x + 3) + (2x − 1)] = 46. Combine inside: 7x + 3 + 2x − 1 = 9x + 2, so 2(9x + 2) = 46, giving 18x + 4 = 46, hence 18x = 42 and x = 42/18 = 7/3. Checking quickly: length = 7*(7/3) + 3 = 58/3, width = 2*(7/3) − 1 = 11/3, sum = 69/3 = 23, and 2×23 = 46, which matches.

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