Answer:
The range of width is 10 ≤ W ≤ 28
Explanation:
* lets study the meaning of compound inequality
- If x is greater than a and x is smaller than b, then x is between a and b
∵ x > a and x < b
∴ The compound inequality is ⇒ a < x < b
# Ex: ∵ x > -2 and x < 10
∴ The compound inequality is ⇒ -2 < x < 10
- If x is greater than or equal a and x is smaller than or equal b, then
x is from a and b
∵ x ≥ a and x ≤ b
∴ The compound inequality is ⇒ a ≤ x ≤ b
# Ex: ∵ x ≥ -2 and x ≤ 10
∴ The compound inequality is ⇒ -2 ≤ x ≤ 10
* Now lets solve the problem
- The garden in the shape of a rectangle with dimensions length (L)
and width (W)
- The length of the garden is 10 feet
- The perimeter (P) of the garden is at least 40 feet and not more than
76 feet
∵ L = 10 feet
∵ P = 2L + 2W
- At least means greater than or equal (≥) and not more than means
smaller than or equal (≤)
∴ P ≥ 40 feet
∴ P ≤ 76 feet
- lets use the rule of the perimeter
∴ 2(10) + 2(W) ≥ 40 ⇒ simplify
∴ 20 + 2W ≥ 40 ⇒ subtract 20 from both sides
∴ 2W ≥ 20 ⇒ divide both sides by 2
∴ W ≥ 10 ⇒ (1)
- Do similar with P ≤ 76
∴ 2(10) + 2(W) ≤ 76 ⇒ simplify
∴ 20 + 2W ≤ 76 ⇒ subtract 20 from both sides
∴ 2W ≤ 56 ⇒ divide both sides by 2
∴ W ≤ 28 ⇒ (2)
- From (1) and (2)
∴ 10 ≤ W ≤ 28 ⇒ compound inequality
* The range of the width is from 10 feet to 28 feet