Inequality
x/11 >= 10
[110, infinity)
6m >= -24
OR
m - 7 < - 12
m >= -4 OR m < -5
(- infinity, -5) U [-4, infinity)
- 8 + b < -3
AND
4b < 20
b < 5 for both
(-infinity, 5)
r + 5 >= 12
OR
r/9 < 0
r >= 7 OR r < 0
(-infinity, 0) U [7, infinity)
|x| <= 8
[-8, 8]
-7n - 10 >= 60
n <= -10
(-infinity, -10]
3 + 7r > 59
OR
-6r - 3 > 33
r > 8 OR r <-6
(-infinity, -6) U (8, infinity)
-6n <= 12
AND
n/3 <= 2
n >= -2 AND n <= 6
(AKA -2 <= n <= 6)
[-2, 6]
Nine less than a number is NO MORE than 8 and is NO LESS than 3
3 <= x - 9 <= 8
Simplified: 12 <= x <= 17
|x + 3| < 4
-4 < x + 3 < 4
-7 < x < 1
(-7, 1)
-(k - 2) > - k - 20
True Statement
All real number (-infinity, infinity)
1 + 5k <= 7k - 3
OR
k - 10 > 2k + 10
k >= 2 OR k < -20
(-infinity, -20) U [2, infinity)
-4 < 8 - 3m <= 11
-1 <= m < 4
[-1, 4)
4n + 8 < 3n - 6
OR
10n - 8 >= 9 + 9n
n < -14 OR n >=17
(-infinity, -14) U [17, infinity)
|2x - 4| > 6
2x - 4 < -6 OR 2x - 4 > 6
x < -1 OR x > 5
(-infinity, -1) U (5, infinity)
-36 + 6x > -8(x + 2) + 4x
x > 2
(2, infinity)
8 - 10r <= 8 + 4r
OR
-6 + 8r < 2 + 8r
True Statements
All Real Numbers (-infinity, infinity)
-16 <= 2n - 10 <= -22
No Solution
False Statement
One half of a number is increased by 3, is greater than zero or less than or equal to negative 3
0.5x + 3 > 0
OR
0.5x + 3 <= -3
-2 + 3|5 - x| <= 4
3|5 - x| <= 6
|5 - x| <= 2
-2 <= 5 - x <= 2
-7 <= -x <= -3
7>= x >= 3
[3,7]
- (4 - 5p) + 3 >= -2(8 - 5p)
p <= 3
(- infinity, 3]
Each type of fish thrives in a specific range of temperatures. The optimum temperatures for sharks range from 18 degrees C to 22 degrees C. Write an inequality that represents the temperature where sharks will NOT thrive.
x < 18 OR x > 22 [degrees C]
2x + 9 >= 10x + 1
AND
3x - 2 < 7x + 2
-1 < x <= 1
(-1, 1]
About 20% of the time you sleep is spend in rapid eye movement (REM) sleep, which is associated with dreaming. If an adult sleeps between 7 and 8 hours, how much time is spent in REM sleep?
7 < 5h < 8
Simplified: 1.4 < h < 1.6
4 - 6|-6 - 3x| <= -5
- 6|-6 - 3x| <= -9
|-6 - 3x| >= 9/6 (or 3/2 = 1-1/2)
-3/2 >= -6 - 3x OR 3/2 <= -6 - 3x
9/2 >= - 3x OR 15/2 <= -3x
-9/6 <= x OR -15/6 >= x
(-infinity, -5/2] U [-3/2, infinity)