Cypress College Math Review: Absolute Value Inequalities
Absolute Value as Distance from the origin
Inequalities of the form
Ex 1)
Ex 3)
x 3
4  x2
CCMR Absolute Value Inequalities
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X c
Ex 2)
x5 4 8
Ex 4)
3 x  2 1  7
Inequalities of the form
Ex 5)
Ex 7)
X c
x 6
Ex 6)
x 3 6  8
2 3x  1  4  6
Ex 8)
4  2 x  12
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Negative numbers and zero
We have covered X  c and X  c where c is a positive number. Now, what if c
is a negative number or zero?
Ex 9)
Ex 10)
|X| < negative
|X| < negative
Ex 11) |X| < zero
Ex 12) |X| > negative
Ex 13) |X| > negative
Ex 14) |X| > zero
Extra practice problems
1.
2.
3.
4.
5.
6.
x7 3 4
6  3x  7
2 x  4  6  10
x 1  5  2
x  5  4
x2 3 7
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Answers to practice problems
1.
2.
3.
 6,8
 1 13 
 , 
 3 3
 , 0  4,  
4. All real numbers
5. No solution
6.
 , 2 6,  
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Extra Practice – Try these on your own, then check with the answers below.
1. 6 x  35 x  36
2
2. 5 x  21x  4
2
3. 20 x  56 x  15
2
4. 12 x  x  6
2
5. 12 x  16 x  3
2
Answers
1.
2.
3.
4.
5.
 2 x  9  3x  4 
 x  4  5x  1
 2 x  510 x  3
 3x  2  4 x  3
 2 x  3 6 x  1
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