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**Learn to solve equations with integers.**

Today’s Learning Goal Assignment Learn to solve equations with integers.

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Pre-Algebra: 2-4 HW Page 734 (Yes, page 734) #1-53 ODD

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**Solving Equations Containing Integers**

2-4 Solving Equations Containing Integers Pre-Algebra Warm Up Problem of the Day Lesson Presentation

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**2-4 Solving Equations Containing Integers Warm Up**

Pre-Algebra 2-4 Solving Equations Containing Integers Warm Up Add, subtract, multiply, or divide. 41 2. 23 – 19 4 3. 12 · 3 36 4. 6(–7) –42 –64 8 5. –8 6. –250 + (–85) –335

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**+ + = 15 + – = 3 + – = 5 + – = 7 Problem of the Day**

What are the numerical values of the , the , and the ? = 15 – = 3 – = 5 – = 7 = 6, = 4, = 5

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**Learn to solve equations with integers.**

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When you are solving equations with integers, your goal is the same as with whole numbers: isolate the variable on one side of the equation. + – + – + – Recall that the sum of a number and its opposite is 0. When you add the opposite to get 0, you can isolate the variable. 3 + (–3) = 0 a + (–a) = 0

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**Additional Example 1A & 1B: Adding and Subtracting to Solve Equations**

Add 3 to both sides. x = – 3 x – = – 3 Commutative Property B. –5 + r = 9 –5 + r = 9 – r = 9 + 5 Add 5 to both sides. r = 14

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**The variable is already isolated. –6 + 8 = n 2 = n Add integers.**

Additional Example 1C & 1D: Adding and Subtracting to Solve Equations Continued Solve. C. –6 + 8 = n The variable is already isolated. –6 + 8 = n 2 = n Add integers. D. z + 6 = –3 z + 6 = –3 –6 Add –6 to each side. z = –9

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**Solve. A. B. p – 7 = – 9 p – 7 = – 9 p – 7 + 7 = – 9 + 7**

Try This: Example 1A & 1B Solve. A. p – 7 = – 9 p – 7 = – 9 p – = – 9 + 7 Add 7 to both sides. p = –2 p – = – 2 Commutative Property B. –2 + g = 5 –2 + g = 5 – g = 5 + 2 Add 2 to both sides. g = 7

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**The variable is already isolated. –1 + 7 = r**

Try This: Example 1C & 1D Solve. C. –1 + 7 = r The variable is already isolated. –1 + 7 = r 6 = r Add integers. D. a + 9 = –9 a + 9 = –9 –9 Add –9 to each side. a = –18

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**Solve. A. –5x = 35 –5x = 35 –5 Divide both sides by –5. x = –7**

Additional Example 2A: Multiplying and Dividing to Solve Equations Continued Solve. A. –5x = 35 –5x = 35 –5 Divide both sides by –5. x = –7

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**Multiply both sides by –4.**

Additional Example 2B: Multiplying and Dividing to Solve Equations Continued Solve. z –4 B. = 5 – = –4 5 z –4 Multiply both sides by –4. z = –20

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**Solve. A. –7x = 42 –7x = 42 Divide both sides by –7. –7 x = –6**

Try This: Example 2A Solve. A. –7x = 42 –7x = 42 –7 Divide both sides by –7. x = –6

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**Multiply both sides by –3.**

Try This: Example 2 Solve. z –3 B. = 9 – = –3 9 z –3 Multiply both sides by –3. z = –27

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**Additional Example 3: Problem Solving Application**

Sarah heard on the morning news that the temperature had dropped 26 degrees since midnight. In the morning, the temperature was –8°F. What was the temperature at midnight?

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**Understand the Problem**

Additional Example 3 Continued 1 Understand the Problem The answer is the temperature at midnight. List the important information: The temperature dropped 26 degrees since midnight. In the morning it was –8°F. Show the relationship or the information: temperature at midnight morning temperature degrees that temperature dropped – =

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**Additional Example 3 Continued**

2 Make a Plan Write an equation and solve it. Let t represent the temperature at midnight and use the equation model. t – 26 = –8 Solve 3 t – 26 = –8 + 26 Add 26 to both sides. t = 18 The temperature at midnight was 18° F.

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**Additional Example 3 Continued**

4 Look Back The temperature at midnight was positive. Its value is less than the absolute value of the drop in temperature. This makes sense, since the morning temperature was negative.

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Try This: Example 3 Tim has two tug boats in a pulling contest. The boat on the left was pulling with a force of 23 tons. If the net force is 50 tons, what force is the boat on the right exerting on the rope?

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**Understand the Problem**

Try This: Example 3 Continued 1 Understand the Problem The answer is the force that the right tug boat is exerting. List the important information: The boat on the left pulls with a force of 23 tons. The net force is 50 tons. Show the relationship of the information: net force left boat’s force = right boat’s force +

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**Try This: Example 3 Continued**

2 Make a Plan Write an equation and solve it. Let f represent the force in tons. 50 = 23 + f Solve 3 50 = f –23 –23 Add –23 to both sides. 27 = f The right boat is exerting a force of 27 tons. –

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**Try This: Example 3 Continued**

Look Back 4 The left tug boat was pulling at a force of 23 tons to the left. The total force on the tow rope was 50 tons. Since 23 tons is less than half the force, the tug boat on the right was advancing forward in a positive direction while the left tug boat was moving backward in a negative direction.

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Lesson Quiz: Part 1 Solve. 1. t + 9 = –8 t = –17 2. –15 = 3b b = –5 x –4 = –7 x = 28 4. z – 16 = 30 z = 46

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Lesson Quiz: Part 2 5. A roller coaster descends down a hill at a rate of 80 feet per second. The bottom of the hill is 400 feet from the top. How long will it take the coaster riders to reach the bottom? 5 seconds

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