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 x2 CCMR Absolute Value Inequalities Page 1 of 5 X c Ex 2) x5 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 CCMR Absolute Value Inequalities Page 2 of 5 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. x7 3 4 6 3x 7 2 x 4 6 10 x 1 5 2 x 5 4 x2 3 7 CCMR Absolute Value Inequalities Page 3 of 5 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, CCMR Absolute Value Inequalities Page 4 of 5 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 510 x 3 3x 2 4 x 3 2 x 3 6 x 1 CCMR Absolute Value Inequalities Page 5 of 5
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