2 4 Solving Equations Containing Integers Todays Learning

2 -4 Solving Equations Containing Integers Today’s Learning Goal Assignment Learn to solve equations with integers. Pre-Algebra

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

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

2 -4 Solving Equations Containing Integers Warm Up Add, subtract, multiply, or divide. 1. 24 + 17 41 3. 12 · 3 – 64 5. 8 Pre-Algebra 2. 23 – 19 4 36 4. 6(– 7) – 8 6. – 250 + (– 85) – 335 – 42

2 -4 Solving Equations Containing Integers Problem of the Day What are the numerical values of the , and the ? + + = 6, Pre-Algebra + – – – = 15 =3 =5 =7 = 4, =5 ,

2 -4 Solving Equations Containing Integers Learn to solve equations with integers. Pre-Algebra

2 -4 Solving Equations Containing Integers 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. + – + – 0 3 + (– 3) = 0 Recall that the sum of a number and its opposite is 0. When you add the opposite to a + (–a) = 0 get 0, you can isolate the variable. Pre-Algebra

2 -4 Solving Equations Containing Integers Additional Example 1 A & 1 B: Adding and Subtracting to Solve Equations Solve. x– 3=– 6 A. x– 3+3=– 6+3 x=– 3 B. – 5 + r = 9 + 5 r = 14 Pre-Algebra Add 3 to both sides. Commutative Property x– 3+3=– 3 0 Add 5 to both sides.

2 -4 Solving Equations Containing Integers Additional Example 1 C & 1 D: Adding and Subtracting to Solve Equations Continued Solve. C. – 6 + 8 = n 2=n D. Pre-Algebra z+6= – 6 z= – 3 – 6 – 9 The variable is already isolated. Add integers. Add – 6 to each side.

2 -4 Solving Equations Containing Integers Try This: Example 1 A & 1 B Solve. p– 7=– 9 A. p– 7+7=– 9+7 p = – 2 B. – 2 + g = 5 + 2 g=7 Pre-Algebra Add 7 to both sides. Commutative Property p– 7+7=– 2 0 Add 2 to both sides.

2 -4 Solving Equations Containing Integers Try This: Example 1 C & 1 D Solve. C. – 1 + 7 = r 6=r D. Pre-Algebra a + 9 = – 9 – 9 a = – 18 The variable is already isolated. Add integers. Add – 9 to each side.

2 -4 Solving Equations Containing Integers Additional Example 2 A: Multiplying and Dividing to Solve Equations Continued Solve. A. – 5 x = 35 – 5 x = – 7 Pre-Algebra Divide both sides by – 5.

2 -4 Solving Equations Containing Integers Additional Example 2 B: Multiplying and Dividing to Solve Equations Continued Solve. B. z =5 – 4 z – 4 = – 4 5 Multiply both sides by – 4 z = – 20 Pre-Algebra

2 -4 Solving Equations Containing Integers Try This: Example 2 A Solve. A. – 7 x = 42 – 7 x = – 6 Pre-Algebra Divide both sides by – 7.

2 -4 Solving Equations Containing Integers Try This: Example 2 Solve. B. z =9 – 3 z – 3 = – 3 9 Multiply both sides by – 3 z = – 27 Pre-Algebra

2 -4 Solving Equations Containing Integers 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? Pre-Algebra

2 -4 Solving Equations Containing Integers 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 Pre-Algebra – degrees that temperature dropped = morning temperature

2 -4 Solving Equations Containing Integers 2 Additional Example 3 Continued Make a Plan Write an equation and solve it. Let t represent the temperature at midnight and use the equation model. t – 26 = – 8 3 Solve t – 26 = – 8 + 26 t = Add 26 to both sides. 18 The temperature at midnight was 18° F. Pre-Algebra

2 -4 Solving Equations Containing Integers 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. Pre-Algebra

2 -4 Solving Equations Containing Integers 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? Pre-Algebra

2 -4 Solving Equations Containing Integers 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 Pre-Algebra = left boat’s + force right boat’s force

2 -4 Solving Equations Containing Integers 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 3 Solve 50 = 23 + f – 23 27 = f Add – 23 to both sides. The right boat is exerting a force of 27 tons. – Pre-Algebra

2 -4 Solving Equations Containing Integers Try This: Example 3 Continued 4 Look Back 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. Pre-Algebra

2 -4 Solving Equations Containing Integers Lesson Quiz: Part 1 Solve. 1. t + 9 = – 8 2. – 15 = 3 b x 3. = – 7 – 4 4. z – 16 = 30 Pre-Algebra t = – 17 b = – 5 x = 28 z = 46

2 -4 Solving Equations Containing Integers 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 Pre-Algebra