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1.6 Solving Compound Inequalities Understanding that conjunctive inequalities take intersections of intervals and disjunctive inequalities take unions of intervals Part 1: First Box of the Worksheet Part 1 of the presentation will go over completing the first box of the worksheet: “Understanding conjunctive compound inequalities…” 1. Solve the following inequality and sketch the interval that satisfies it: 4 6 2x 4 1. Solve the following inequality and sketch the interval that satisfies it: 4 6 2x 4 Subtract 6 from each component of the equation… 10 2x 2 1. Solve the following inequality and sketch the interval that satisfies it: 4 6 2x 4 Subtract 6 from each component of the equation… 10 2x 2 Divide each component by -2 …remembering to switch the signs. 5 x 1 1. Solve the following inequality and sketch the interval that satisfies it: 4 6 2x 4 Subtract 6 from each component of the equation… 10 2x 2 Divide each component by -2 …remembering to switch the signs. 5 x 1 Or 1 x 5 1. Solve the following inequality and sketch the interval that satisfies it: 4 6 2x 4 Subtract 6 from each component of the equation… 10 2x 2 Divide each component by -2 …remembering to switch the signs. 5 x 1 Or 1 x 5 Sketch the interval: 2-4. A conjunctive inequality is the intersection of two intervals. 2. Solve and sketch the interval. 4 6 2x 3. Solve and sketch the interval. 6 2x 4 2-4. A conjunctive inequality is the intersection of two intervals. 2. Solve and sketch the interval. 4 6 2x Subtract 6 10 2x 3. Solve and sketch the interval. 6 2x 4 2-4. A conjunctive inequality is the intersection of two intervals. 2. Solve and sketch the interval. 4 6 2x Subtract 6 10 2x Divide by -2 5 x 3. Solve and sketch the interval. 6 2x 4 2-4. A conjunctive inequality is the intersection of two intervals. 2. Solve and sketch the interval. 4 6 2x Subtract 6 10 2x Divide by -2 5 x Or x5 3. Solve and sketch the interval. 6 2x 4 2-4. A conjunctive inequality is the intersection of two intervals. 2. Solve and sketch the interval. 4 6 2x Subtract 6 10 2x Divide by -2 5 x Or x5 3. Solve and sketch the interval. 6 2x 4 2-4. A conjunctive inequality is the intersection of two intervals. 2. Solve and sketch the interval. 4 6 2x Subtract 6 10 2x Divide by -2 5 x Or x5 3. Solve and sketch the interval. 6 2x 4 Subtract 6 2x 2 Divide by -2 x 1 2-3. Solve and sketch each of the two inequalities separately. 2. Solve and sketch the interval. 4 6 2x Subtract 6 10 2x Divide by -2 5 x Or x5 3. Solve and sketch the interval. 6 2x 4 Subtract 6 2x 2 Divide by -2 x 1 4. The solution to the compound inequality is the intersection of each separate inequality. Each inequality separately: 4 6 2x 6 2x 4 4. The solution to the compound inequality is the intersection of each separate inequality. Each inequality separately: 4 6 2x 6 2x 4 Taking the intersection means considering points that satisfy BOTH inequalities. The first inequality needs to be true and the second one needs to be true. 4 6 2x AND 6 2x 4 4. The solution to the compound inequality is the intersection of each separate inequality. Each inequality separately: 4 6 2x 6 2x 4 Taking the intersection means considering points that satisfy BOTH inequalities. The first inequality needs to be true and the second one needs to be true. 4 6 2x AND 6 2x 4 Part 1: First Box of the Worksheet The point of this exercise is that you can solve the conjunctive compound inequality in two different ways: 1. Solving algebraically by performing operations on all 3 parts of the compound inequality. 2. Solve each simple inequality separately and then taking the intersection of the two intervals. Part 1: First Box of the Worksheet The point of this exercise is that you can solve the conjunctive compound inequality in two different ways: 1. Solving algebraically by performing operations on all 3 parts of the compound inequality. 2. Solve each simple inequality separately and then taking the intersection of the two intervals. The first way is easier for solving conjunctive inequalities. However, disjunctive inequalities can only be solved by solving each simple inequality separately and then taking their union. Part 2: Second Box of the Worksheet Part 2 of the presentation will go over using unions to solve disjunctive compound inequalities: “Solving disjunctive compound inequalities…” Solve 3x 6 OR x 1 0 1. Solve and sketch the interval. 3x 6 2. Solve and sketch the interval. x 1 0 Solve 3x 6 OR x 1 0 1. Solve and sketch the interval. 3x 6 Divide by 3 x 2 2. Solve and sketch the interval. x 1 0 Solve 3x 6 OR x 1 0 1. Solve and sketch the interval. 3x 6 Divide by 3 x 2 2. Solve and sketch the interval. x 1 0 Solve 3x 6 OR x 1 0 1. Solve and sketch the interval. 3x 6 Divide by 3 x 2 2. Solve and sketch the interval. x 1 0 Add 1 … x 1 Solve 3x 6 OR x 1 0 1. Solve and sketch the interval. 3x 6 Divide by 3 x 2 2. Solve and sketch the interval. x 1 0 Add 1 … x 1 Solve 3x 6 OR x 1 0 The ‘or’ means that either the left inequality needs to be true OR the right inequality needs to be true. Solve 3x 6 OR x 1 0 The ‘or’ means that either the left inequality needs to be true OR the right inequality needs to be true. Thus, we want all the points that make the left inequality true together with all the points that make the right inequality true – we take the union of the two intervals. The union is: Solve 3x 6 OR x 1 0 The ‘or’ means that either the left inequality needs to be true OR the right inequality needs to be true. Thus, we want all the points that make the left inequality true together with all the points that make the right inequality true – we take the union of the two intervals. The union is: Solve 3x 6 OR x 1 0 The ‘or’ means that either the left inequality needs to be true OR the right inequality needs to be true. Thus, we want all the points that make the left inequality true together with all the points that make the right inequality true – we take the union of the two intervals. The union is: In interval notation this is: (-∞,2](1, ∞).

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posted: | 8/18/2012 |

language: | English |

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