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**2-5 Lesson Presentation Solving Inequalities Containing Integers**

Course 3 Lesson Presentation

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**2-5 Learn to solve inequalities with integers.**

Course 3 2-5 Solving Inequalities Containing Integers Learn to solve inequalities with integers.

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**2-5 Solving Inequalities Containing Integers**

Course 3 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. Adding rock salt to the ice lowers the freezing point and helps to freeze the ice cream mixture. 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.

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**2-5 Solving Inequalities Containing Integers**

Course 3 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.

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**2-5 Solving Inequalities Containing Integers**

Course 3 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!

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**Additional Example 1A: Adding and Subtracting to Solve Inequalities**

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

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**2-5 Solving Inequalities Containing Integers Solve and graph.**

Course 3 2-5 Solving Inequalities Containing Integers Additional Example 1B: Adding and Subtracting to Solve Inequalities Continued Solve and graph. B. r – 9 12 r – 9 12 r – Add 9 to both sides. r 21 15 21 24

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**Solving inequalities is almost identical to solving equations :**

Even Better News ! Solving inequalities is almost identical to solving equations : Example 1 x is any value less than 4 28-Mar-17

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**Solving inequalities is almost identical to solving equations :**

Example 2 x is any value greater than or equal to 5 28-Mar-17

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**2-5 Solving Inequalities Containing Integers 5 > –1**

Course 3 2-5 Solving Inequalities Containing Integers 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 5 is greater than –1. –1 • 5 –1 • (–1) Multiply both sides by –1. – > or < ? –5 < 1 You know –5 is less than 1, so you should use <. –5 < 1 –7 –6 –5 –4 –3 –2 – 5 > –1

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**MULTIPLYING INEQUALITIES BY NEGATIVE INTEGERS**

Course 3 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.

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Course 3 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

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**Additional Example 2: Multiplying and Dividing to Solve Inequalities**

Course 3 2-5 Solving Inequalities Containing Integers Additional Example 2: Multiplying and Dividing to Solve Inequalities Solve and graph. A. –3y 15 Divide each side by –3; changes to . –3y 15 –3 –7 –5 4 y –5 B. 7m < 21 7m < 21 7 Divide each side by 7. 3 –3 5 m < 3

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**> Solving Inequalities 8 – 3m < 2 -3m < -6 -3 So m > 2**

The only one to watch out for is when you are dividing by a negative Example 8 – 3m < 2 -3m < -6 Subtract 8 from each side m -6 -3 > Divide across by -3 and change the Sign So m > 2 28-Mar-17

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**≤ Solving Inequalities 5( x – 1 ) - 8x ≥ - 17 5x – 5 – 8x ≥ - 17**

Example 2 5( x – 1 ) - 8x ≥ - 17 5x – 5 – 8x ≥ - 17 - 3x - 5 ≥ - 17 - 3x ≥ - 12 x -3 ≤ So x ≤ 4 28-Mar-17

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**2-5 –2 –3 –3 Solving Inequalities Containing Integers Solve and graph.**

Course 3 2-5 Solving Inequalities Containing Integers Lesson Quiz: Part 1 Solve and graph. 1. h + 2 < 0 –2 2 h –2 2. c – 5 > –2 3 –3 c 3 t –3 < 1 3 –3 t > –3 4. 7n > 28 4 8 n > 4

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**2-5 5. x 2°F Solving Inequalities Containing Integers**

Course 3 2-5 Solving Inequalities Containing Integers Lesson Quiz: Part 2 5. 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? x 2°F

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