Absolute Value
|2x+3|< 5
-4<x<1
1/2 < c - 3/4
c > 5/4
x < -2 or x > 2
Use substitution
y = 6x
2x + 3y = -20
(-1,-6)
SOLVE BY ELIMINATION
2x + 5y = -3
-2x +2y = 6
(6,-3)
|2z-9| < 1
4<z<5
Twelve is at most a number decreased by 7. (simplify)
19 < x
(Graph) 9|9 + 3x| < 81
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-6 0
- 6 < x < 0
3x - y = -2
3x - y = 0
Find the slope, x- intercept, and y - intercept
1/2 x - 2y = -4
x intercept (-8,0) y - intercept (0,2)
slope 1/4
|3 - 2r| >7
r<-2 or r > 5
2/3n > - 12
n > -18
-5| 4x + 4| > -60
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-4 2
-4 < x < 2
SOLVE BY SUBSTITUTION
x + 2y = 13
-2x - 3y = -18
(-3, 8)
-4 < -2x - 4 < 12
(Solve the ineqality)
-8< x < 0
| -4 + 8k| = 68
k= 9 k=-8
k - 3 < -7 or k + 5 > 8
k < -4 or k > 3
|-3n + 6| - 9 > 15
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- 6 10
n < -6 or n > 10
USE ELIMINATION
x - y = 1
x + y = -9
(-4, -5)
One number added to three times another number is 24. Five times the first number added to three times the other number is 36. Find the numbers.
First number is 3. Second number is 7.
(3,7)
-2| -2p - 8 | > -56
-18 < p < 10
2c - 4 > -6 and 3c + 1 < 13
-1 < c < 4
-1 + |3 - 2x| < 14
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-6 9
-6 < x < 9
USE ELIMINATION
4x + y = 23
3x - y = 12
(5,3)
Nick plans to start a dog-treat business. He figures it will cost $20 in operating costs plus $0.50 to product each treat. He plans to sell the treats for $1.50. How many treats does Nick need to sell per week to break even?
20 treats for $30