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Pre-Algebra 2-5 Solving Inequalities Containing Integers Pre-Algebra: 2-5 HW Page 80 #13-30 all

Pre-Algebra 2-5 Solving Inequalities Containing Integers Today’s Learning Goal Assignment Learn to solve inequalities with integers.

Pre-Algebra 2-5 Solving Inequalities Containing Integers 2-5 Solving Inequalities Containing Integers Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Pre-Algebra 2-5 Solving Inequalities Containing Integers Warm Up Compare, Use >, <, or =. Pre-Algebra 2-5 Solving Inequalities Containing Integers > > = < > 1. –3 –42. 6 –2 3. –8 –54. –5 – –36. –8 –2 <

Pre-Algebra 2-5 Solving Inequalities Containing Integers Problem of the Day Elliot led the race; Gordon was ahead of Wallace. Labonte was directly behind Gordon and directly ahead of Marlin. Who was in last place ? Wallace

Pre-Algebra 2-5 Solving Inequalities Containing Integers Today’s Learning Goal Assignment Learn to solve inequalities with integers.

Pre-Algebra 2-5 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 water’s 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.

Pre-Algebra 2-5 Solving Inequalities Containing Integers 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? 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.

Pre-Algebra 2-5 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!

Pre-Algebra 2-5 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

Pre-Algebra 2-5 Solving Inequalities Containing Integers B. r – 9  12 r  21 Add 9 to both sides. r –  r – 9  Additional Example 1B: Adding and Subtracting to Solve Inequalities Continued Solve and graph.

Pre-Algebra 2-5 Solving Inequalities Containing Integers C. u – 5  3 u  8 Add 5 to both sides. u –  u – 5  Solve and graph. Additional Example 1C: Adding and Subtracting to Solve Inequalities Continued

Pre-Algebra 2-5 Solving Inequalities Containing Integers c  –4 D. c + 6  2 Subtract 6 from both sides. –6 c + 6  2 04 –7 –4 Solve and graph. Additional Example 1D: Adding and Subtracting to Solve Inequalities Continued

Pre-Algebra 2-5 Solving Inequalities Containing Integers y  –8 A. y + 7  –1 Subtract 7 from both sides. –7 y + 7  –1 Try This: Example 1A 0 –11 –8 Solve and graph.

Pre-Algebra 2-5 Solving Inequalities Containing Integers B. f – 4  8 r  12 Add 4 to both sides. f –  f – 4  Try This: Example 1B Solve and graph.

Pre-Algebra 2-5 Solving Inequalities Containing Integers C. r – 2 < 1 r < 3 Add 2 to both sides. r – < r – 2 < 1 –303 8 Try This: Example 1C Solve and graph.

Pre-Algebra 2-5 Solving Inequalities Containing Integers d  –3 D. d + 9  6 Subtract 9 from both sides. –9 d + 9  6 –30 –74 Try This: Example 1D Solve and graph.

Pre-Algebra 2-5 Solving Inequalities Containing Integers –5 1 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

Pre-Algebra 2-5 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.

Pre-Algebra 2-5 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

Pre-Algebra 2-5 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

Pre-Algebra 2-5 Solving Inequalities Containing Integers A. –8y  24 y  –3 Divide each side by –8; changes > to <. B. 9f > 45 f > 5f > 5 Divide each side by 9. Try This: Example 2 –8y  24 –8–8–8–8 9f > –3 0 – Solve and graph.

Pre-Algebra 2-5 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–

Pre-Algebra 2-5 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