Download 2.9 Solving Linear Inequalities Linear Inequality‐is an

2.9 Solving Linear Inequalities Linear Inequality‐is an inequality that can be written in the form ax + b > c , where a, b and c are real numbers and a ≠ 0 A. Graphing Inequalities on a Number Line Example 1. Graph each inequality on a number line. 1. x > ‐5 -2
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-6
-4
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2. − ≥ m -2
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2
-6
-4
4
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3. − 4 < t ≤ 2 -2
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-6
-4
4
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B. Solving the Inequalities using the Addition and Multiplication Property of Inequality Solution of an Inequality­is a value of the variable that makes the inequality a true statement. Two ways of writing the solution set of an inequality 1. Set Builder­Notation: Example: 2. Interval Notation: Example: Properties of Inequalities—Let a, b and c be real numbers, then 1. Addition Property: If a < b , then a + c < b + c and If a > b , then a + c > b + c . 2. Positive Multiplication Property: (c is positive) If a < b , then ac < bc and If a > b , then ac > bc . 3. Negative Multiplication Property: (c is negative) If a < b , then ac > bc and If a > b , then ac < bc . Note: If multiply or divide by a negative number, the inequality sign change to opposite. Example 2. Solve each inequality. Graph the solution set. 1. − 4a − 2 > −5a + 1 -6
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-2
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2. − x ≤ 9 5
-20
-10
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30
-6
-4
-2
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-6
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3. − 18( y − 2 ) ≥ −21 y + 24 4. -30
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(x + 2) > 1 (x + 3) 21
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C. Solving Applications Involving Inequalities Key words: Is less than means < At most means ≤ Is greater than means > At least means ≥ Is less than or equal to means ≤ Is greater than or equal to means ≥ No more than means ≤ Not equal to means ≠ Example 3. Set up an inequality and solve the following. 1. Eight more than twice a number is less than negative twelve. Find all numbers that make this statement true. 2. One side of a triangle is six times as long as another sides, and the third side is 8 inches long. If the perimeter can be no more than 106 inches, find the maximum lengths of the other two sides. 3. In order to earn an A in a course, a student must have an average on 3 exams of at least 90. If a student scores 86 and 88 on the first two tests, describe the range of scores that the student needs on the third test in order to earn an A in the course.