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

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}

w + 7 = length

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**