Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Add, subtract, multiply, or divide. Warm Up Add, subtract, multiply, or divide. 1. 24 + 17 41 2. 23 – 19 4 3. 12  3 36 4. 6(–7) –42 –64 8 5. –8 6. –250 + (–85) –335 2

Problem of the Day Janie’s horse refused to do 5 jumps today and cleared 14 jumps. Yesterday, the horse cleared 9 more jumps than today. He won 3 first place ribbons. How many jumps did the horse clear in the two-day jumping event? 37

Learn to solve equations using addition and subtraction.

Vocabulary equation inverse operation

An equation is a mathematical sentence that uses an equal sign to show that two expressions have the same value. All of these are equations. 100 2 = 50 3 + 8 = 11 r + 6 = 14 24 = x – 7 To solve an equation that contains a variable, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation.

Additional Example 1: Determining Whether a Number is a Solution of an Equation Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. x + 8 = 15 5 + 8 = 15 Substitute 5 for x. 13= 15  So 5 is not solution.

Additional Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. x + 8 = 15 7 + 8 = 15 Substitute 7 for x. 15= 15  So 7 is a solution.

Additional Example 1 Continued Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Substitute each value for x in the equation. x + 8 = 15 23 + 8 = 15 Substitute 23 for x. 31= 15  So 23 is not a solution.

Check It Out: Example 1 Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Substitute each value for x in the equation. x – 4 = 13 9 – 4 = 13 Substitute 9 for x. 5 = 13  So 9 is not a solution.

Check It Out: Example 1 Continued Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Substitute each value for x in the equation. x – 4 = 13 27 – 4 = 13 Substitute 27 for x. 23 = 13  So 27 is not a solution.

Check It Out: Example 1 Continued Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Substitute each value for x in the equation. x – 4 = 13 17 – 4 = 13 Substitute 17 for x. 13 = 13  So 17 is a solution.

Addition and subtraction are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. In other words, get the variable alone on one side of the equal sign.

To solve a subtraction equation, like y – 15 = 7, you would use the Addition Property of Equality.

There is a similar property for solving addition equations, like x + 9 = 11. It is called the Subtraction Property of Equality.

Additional Example 2A: Solving Equations Using Addition and Subtraction Properties Solve. 10 + n = 18 Use the Subtraction Property of Equality: Subtract 10 from both sides. 10 + n = 18 –10 –10 n = 8 Check 10 + n = 18 10 + 8 = 18 Substitute 8 for n. 18 = 18 

Additional Example 2B: Solving Equations Using Addition and Subtraction Properties Solve. p – 8 = 9 p – 8 = 9 Use the Addition Property of Equality: Add 8 to both sides. + 8 + 8 p = 17 Check p – 8 = 9 17 – 8 = 9 Substitute 17 for p. 9 = 9 

Additional Example 2C: Solving Equations Using Addition and Subtraction Properties Solve. 22 = y – 11 22 = y – 11 Use the Addition Property of Equality: Add 11 to both sides. + 11 + 11 33 = y Check 22 = y – 11 22 = 33 – 11 Substitute 33 for y. 22 = 22 

Check It Out: Example 2A Solve. 15 + n = 29 15 + n = 29 Use the Subtraction Property of Equality: Subtract 15 from both sides. –15 –15 n = 14 Check 15 + n = 29 10 + 14 = 29 Substitute 14 for n. 29 = 29 

Check It Out: Example 2B Solve. p – 6 = 7 p – 6 = 7 Use the Addition Property of Equality: Add 6 to both sides. + 6 + 6 p = 13 Check p – 6 = 7 13 – 6 = 7 Substitute 13 for p. 7 = 7 

Check It Out: Example 2C Solve. 44 = y – 23 44 = y – 23 Use the Addition Property of Equality: Add 23 to both sides. + 23 + 23 67 = y Check 44 = y – 23 44 = 67 – 23 Substitute 67 for y. 44 = 44 

Additional Example 3: Problem Solving Application Jan and Alex are arguing over who gets to play a board game. If Jan, on the right, pulls with a force of 14 N, what force is Alex exerting on the game if the net force is 3 N? 22

Force is measured in newtons (N). The number of newtons tells the size of the force and the sign tells the direction. Positive is to the right, and negative is to the left. Helpful Hint!

Understand the Problem Additional Example 3 Continued 1 Understand the Problem The answer is the force that Alex, on the left, is exerting on the board game. List the important information: Jan, on the right pulls with a force of 14 N. The net force is 3 N. Show the relationship or the information: Net force Alex’s force Jan’s force = + 24

Additional Example 3 Continued 2 Make a Plan Write an equation and solve it. Let f represent Alex’s force on the board game, and use the equation model. 3 = f + 14 Solve 3 3 = f + 14 – 14 Subtract 14 from both sides. –11 = f Alex was exerting a force of –11 N on the board game. 25

Additional Example 3 Continued 4 Look Back Check the answer by using a number line. Move 14 units right to show Jan's force. Move 11 units to the left to show Alex's force. 11 14 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 26

Check It Out: Example 3 Frankie and Carol are playing tug of war using a rope. If Frankie, on the right, pulls with a force of 7 N, what force is Carol exerting on the game if the net force is 4 N? 27

Understand the Problem Check It Out: Example 3 Continued 1 Understand the Problem The answer is the force that Carol, on the left is exerting on the rope. List the important information: Frankie, on the right pulls with a force of 7 N. The net force is 4 N. Show the relationship or the information: Net force Carol’s force Frankie’s force = + 28

Check It Out: Example 3 Continued 2 Make a Plan Write an equation and solve it. Let f represent Carol’s force on the rope, and use the equation model. 4 = f + 7 Solve 3 4 = f + 7 – 7 Subtract 7 from both sides. –3 = f Carol was exerting a force of -3 N on the rope. 29

Check It Out: Example 3 Continued 4 Look Back Check the answer by using a number line. Move 7 units right to show Frankie's force. Move 3 units to the left to show Carol's force. 3 7 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 30