Inequality FAQ
Draw the less than symbol
<
-5 < 2x+1 ≤ 7
−3 < x ≤ 3
The area of a rectangle is given by:
A = length × width
Suppose a rectangular garden has a fixed width of 4 meters, and the length must be such that the area is between 40 and 100 square meters, inclusive.
Set Up: 40 ≤ 4A ≤ 100
Answer: 10 ≤ A ≤ 25
Draw the greater than symbol
>
−4 ≤ 3x−1 < 5
−1 ≤ x< 2
A banner is shaped like a rectangle. Its width is 2.5 feet, and the area must be between 15 and 40 square feet, inclusive.
Set up: 15 ≤ 2.5A ≤ 40
Answer: 6 ≤ A ≤ 16
When do you use an open circle?
less than/greater than signs
0 ≤ 5−2x < 10
5/2 ≥ x > -5/2
2.5 ≥ x > -2.5
A rectangular rug has a length of 8 feet. The area must be more than 48 but no more than 80 square feet.
Set up: 48< 8w ≤ 80
Answer: 6< w ≤ 10
When do you use a closed circle?
less than or equal to/greater than or equal to signs
−7 < 2−x ≤ 1
9 > x ≥ 1
A farmer is building a rectangular chicken pen with a fixed area between 120 and 200 square meters, not including the endpoints. The width is 6 meters.
Set Up: 120 < 6A < 200
Answer: 20 < A < 33.333333
Answer: 20 < A < 200/6
describe "and/or" compound inequality graphs
and --graph meets in the middle
or --graph goes in 2 directions
−6 < 2(3x−1) ≤ 10
−2/3 < x ≤ 2
−0.67 < x ≤ 2
A picture frame is rectangular. Its width is fixed at 6 inches. The length of the frame needs to be such that the area of the frame is between 48 and 96 square inches, inclusive.
Set Up: 48 ≤ 6A ≤ 96
Answer: 8 ≤ A ≤ 16