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2-5 Solving Inequalities Containing Integers Course 3 Lesson Presentation Lesson Presentation

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Learn to solve inequalities with integers. Course Solving Inequalities Containing Integers

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Course Solving Inequalities Containing Integers When you pour salt on ice, the ice begins to melt. If enough salt is added, the resulting saltwater will have a freezing point of –21°C, which is much less than waters freezing point of 0°C. At its freezing point, a substance begins to freeze. To stay frozen, the substance must maintain a temperature that is less than or equal to its freezing point. Adding rock salt to the ice lowers the freezing point and helps to freeze the ice cream mixture.

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If you add salt to the ice that is at a temperature of –4°C, what must the temperature change be to keep the ice from melting? Course Solving Inequalities Containing Integers This problem can be expressed as the following inequality: –4 + t –21 When you add 4 to both sides and solve, you find that if t –21, the ice will remain frozen.

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Course Solving Inequalities Containing Integers The graph of an inequality shows all of the numbers that satisfy the inequality. When graphing inequalities on a number line, use solid circles ( ) for and and open circles ( ) for > and <. Remember!

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Course Solving Inequalities Containing Integers k > –5 A. k +3 > –2 Subtract 3 from both sides. –3 k +3 > –2 Solve and graph. Additional Example 1A: Adding and Subtracting to Solve Inequalities –5 0

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Course Solving Inequalities Containing Integers B. r – 9 12 r 21 Add 9 to both sides. r – r – Additional Example 1B: Adding and Subtracting to Solve Inequalities Continued Solve and graph.

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15-Feb-14 Solving inequalities is almost identical to solving equations : Solving Inequalities Example 1 x is any value less than 4 Even Better News !

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15-Feb-14 Solving inequalities is almost identical to solving equations : Solving Inequalities Example 2 x is any value greater than or equal to 5

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–5 1 Course Solving Inequalities Containing Integers 5 is greater than –1. Sometimes you must multiply or divide to isolate the variable. Multiplying or dividing both sides of an inequality by a negative number gives a surprising result. 5 > –1 Multiply both sides by –1. –1 5 –1 (–1) > or < ? You know –5 is less than 1, so you should use <. –5 < 1 –7 –6 –5 –4 –3 –2 – –5 < 1 5 > –1

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Course Solving Inequalities Containing Integers 3 > 1 –4 12 Multiply by –2 Divide by –4 1 –3 –6 < –2 MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS Words Original Inequality Multiply/ Divide Result Multiplying or dividing by a negative number reverses the inequality symbol.

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Course Solving Inequalities Containing Integers The direction of the inequality changes only if the number you are using to multiply or divide by is negative. Helpful Hint

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Course Solving Inequalities Containing Integers A. –3y 15 y –5 Divide each side by –3; changes to. B. 7m < 21 m < 3m < 3 Divide each side by 7. Additional Example 2: Multiplying and Dividing to Solve Inequalities Solve and graph. 0 3–3 5 –3y 15 –3–3–3–3 7m < –7 –5 04

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15-Feb-14 Solving Inequalities The only one to watch out for is when you are dividing by a negative Example 8 – 3m < 2 -3m < -6 m Subtract 8 from each side Divide across by -3 and change the Sign So m > 2 >

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15-Feb-14 Solving Inequalities Example 2 5( x – 1 ) - 8x x – 5 – 8x x x - 12 x So x 4

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Course Solving Inequalities Containing Integers Lesson Quiz: Part 1 Solve and graph. 1. h + 2 < 0 2. c – 5 > –2 7n > 28 t –3 3. < 1 h –2 n > 4 t > –3 c 3 –2– –3–3 0 3 –3–

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Course Solving Inequalities Containing Integers A local weather forecast stated that it would be 12°F tonight and at least 10° colder the next night. Write an inequality to show how cold it will be ? Lesson Quiz: Part 2 5. x 2°F

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