Width and length of rectangle written as compound inequalities

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

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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}
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The graphing is up to you.

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