The length of a rectangle is 7 inches longer than the width the perimeter is between 29 and 40 inches.
A. Write the width as a compound inequality and then graph the results B. Write the length as a compound inequality and then graph the results
w = width
w + 7 = length {length is 7 inches longer than width} Perimeter of a rectangle = 2(width) + 2(length) Perimeter = 2w + 2(w + 7) = 2w + 2w + 14 {used distributive property} = 4w + 14 {combined like terms} Perimeter 29 < 4w + 14 < 40 {perimeter is between 29 and 40 inches} Width 29 < 4w + 14 < 40 15 < 4w < 26 {subtracted 14 from left, middle, and right} 15/4 < w < 13/2 {divided left, middle, and right by 4} Length 15/4 < w < 13/2 {width inequality from previous step} 43/4 < w + 7 < 27/2 {added 7 to left, middle, and right} The graphing is up to you. Ask the House
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January 2021
