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# section17 - For a b c and d real numbers 1 If a< b and...

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MAT 111 - College Algebra Section 1.7 - Linear Inequalities in One Variable An inequality is an expression that involves the symbol(s) < , > , or . A solution set of an inequality is the set of all real numbers that are solutions to the inequality. That is, they are values that make the inequality a true statement. Graph of an inequality is the set of all points on the real number line that represent the solution set. It consists of intervals which may be bounded or unbounded . Examples: Write out an inequality that represents the interval and state whether the interval is bounded or unbounded. 1. (2 , 10] 2. [ - 5 , ) 3. ( -∞ , 7] Properties of Inequalities:

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Unformatted text preview: For a, b, c, and d real numbers 1. If a < b and b < c , then a < c . 2. If a < b and c < d , then a + c < b + d . 3. If a < b , then a + c < b + c . 4. If a < b and (a) c > 0, then ac < bc . (b) c < 0, then ac > bc . Examples: Solve the following inequality and sketch the solution on the real line. 1. 10 x <-40. 2.-6 x > 15. 3. x + 7 ≤ 12. 4. 3 x + 1 ≥ 2 + x . 5. 6 x-4 ≤ 2 + 8 x . 6. 0 ≤ x + 3 2 < 5 Inequalities Involving Absolute Values: for a ≥ (a) | x < a if and only if-a < x < a . (b) | x | > a if and only if x > a or x <-a . 7. | x 5 | > 3. 8. 3 | 4-5 x | ≤ 9....
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section17 - For a b c and d real numbers 1 If a< b and...

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