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Solving Equations by Adding and Subtracting: Vocabulary Solve: To solve an equation mean to find a solution to the equation. Isolate the variable: Get the variable alone on one side of the equal sign. Addition Property of Equality: You can add the same amount to both sides of an equation, and the statement will still be true.

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Vocabulary Cont… Subtraction Property of Inequality: You can subtract the same amount from both sides of an equation, and the statement will still be true. Inverse Operations: Operations that undo each other: addition and subtraction, multiplication and division are inverse operations of each other.

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Addition Property of Equality WordsNumbersAlgebra You can add the same amount to both sides of and the statement will still be true 2 + 3 = 5 + 4 = +4 2 + 7 = 9 x = y + z + z x + z = y + z

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Solving an Equation by Addition Solve the equation x – 8 = 17. Check your answer. x - 8 = 17 + 8 + 8 x = 25 Check Your Answer: 25 - 8 = 17 17 = 17

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Subtraction Property of Equality WordsNumbersAlgebra You can subtract the same amount from both sides of an equation and the statement will still be true. 4 + 7 = 11 - 3 = - 3 4 + 4 = 8 8 = 8 x = y - z = - z x - z = y - z

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Solve an Equation by Subtraction Solve the equation a + 5 = 11. Check your answer. a + 5 = 11 - 5 - 5 a = 6 Check your answer. 6 + 5 = 11 11 = 11

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Solve an Equation by Addition with Integers Example: Solve for x x - 8 = -6 1. What does it mean to isolate the variable? * Get the variable alone by moving everything else to other side of the equals sign. 2. What is the inverse operation we are going to use? *We are going to use the inverse of subtracting 8, which is adding 8

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Solve an Equation by addition with Integers x - 8 = -6 + 8 + 8 x = 2 Check your answer: 2 - 8 = -6 -6 = -6

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Solve an Equation by Subtracting with Integers Example: Solve for m 8 + m = 3 1. What does it mean to isolate the variable? * Get the variable alone by moving everything else to other side of the equals sign. 2. What is the inverse operation we are going to use? *We are going to use the inverse of adding 8, which is subtracting 8.

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Solve an Equation by Subtracting with Integers 8 + m = 3 - 8 - 8 m = -5 Check your answer: 8 + -5 = 3 3 = 3

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Mixed Examples 1. -4 + n = 2 2. k - 15 = -20 3. 7 - a = -3 4. -29 + p = -32 Solutions: 1. 6 2. -5 3. 10 4. -3

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Solving Equations by Multiplying What does it mean to isolate the variable? What is the inverse operation for multiplication? How can you use the inverse operation of multiplication to solve an equation?

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Solving an Equation by Multiplying Example: Solve for x x = 12 7 (7) x = 12 (7) 7 x = 84 Check your answer 84 = 12 7 12 = 12

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Solving an Equation by Multiplying Example: Solve for m m = -5 5 (5) m = -5 (5) 5 m = -25 Check your answer -25 = -5 5 -5 = -5

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Solving an Equation by Division What does it mean to isolate the variable? What is the inverse operation for division? How can you use the inverse operation of division to solve an equation?

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Solving an Equation by Division Example: Solve for p 12p = 144 12 12 p = 12 Check your answer 12(12) = 144 144 = 144

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Solving an Equation by Division Example: Solve for r -9r = -81 -9 -9 r = 9 Check your answer -9(9) = -81 -81 = -81

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Practice Problems 8x = 96 -4m = -60 p = 3 6 n = -12 -12 12 15 18 144

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