Word Problem with Perimeter

The perimeter of a rectangular field is 504 yards. It's length is 6 yards shorter than twice it's width? What is the area? 

x = width
2x - 6 = length {six yards shorter than twice the width} 

2(x) + 2(2x - 6) = 504 {two times width + two times length = perimeter}
2x + 4x - 12 = 504 {used distributive property}
6x - 12 = 504 {combined like terms}
6x = 516 {added 12 to both sides}
x = 86 {divided both sides by 6}
2x - 6 = 166 {substituted 86 for x into 2x - 6} 

width = 86 yards
length = 166 yards
area = 14,276 yds² {area is length x width}

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