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1-3 Solving Addition and Subtraction Equations Pre-Algebra Warm Up Write an algebraic expression for each word phrase. 1. a number x decreased by times the sum of p and plus the product of 8 and n 4. the quotient of 4 and a number c x 9 5(p + 6) 2 + 8n 4 c 1-3 Solving Addition and Subtraction Equations Pre-Algebra

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Learn to solve equations using addition and subtraction.

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Vocabulary equation solve solution inverse operation isolate the variable Addition Property of Equality Subtraction Property of Equality

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1-3 Solving Addition and Subtraction Equations Pre-Algebra An equation uses an equal sign to show that two expressions are equal. All of these are equations = 11r + 6 = 1424 = x – = 50 To solve an equation, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation.

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Additional Example 1: Determining Whether a Number is a Solution of an Equation Substitute each value for x in the equation. Substitute 5 for x. 13= 15 ? So 5 is not solution. x + 8 = 15 ? = 15 ?

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Additional Example 1 Continued Substitute each value for x in the equation. Substitute 7 for x. 15= 15 ? So 7 is a solution. x + 8 = 15 ? = 15 ?

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Additional Example 1 Continued Substitute each value for x in the equation. Substitute 23 for x. 31= 15 ? So 23 is not a solution. x + 8 = 15 ? = 15 ?

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Addition and subtraction are inverse operations, which means they undo each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign.

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1-3 Solving Addition and Subtraction Equations Pre-Algebra To solve a subtraction equation, like y 15 = 7, you would use the Addition Property of Equality. You can add the same number to both sides of an equation, and the statement will still be true = = 9 x = y + z ADDITION PROPERTY OF EQUALITY WordsNumbersAlgebra

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1-3 Solving Addition and Subtraction Equations Pre-Algebra There is a similar property for solving addition equations, like x + 9 = 11. It is called the Subtraction Property of Equality. You can subtract the same number from both sides of an equation, and the statement will still be true = = 8 x = y z z SUBTRACTION PROPERTY OF EQUALITY WordsNumbersAlgebra

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Solve. Additional Example 2A: Solving Equations Using Addition and Subtraction Properties Subtract 10 from both sides. A n = n = 18 – n = 8 n = 8 Identity Property of Zero: 0 + n = n. Check 10 + n = 18 ? = = 18 ?

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Solve. Additional Example 2B: Solving Equations Using Addition and Subtraction Properties Add 8 to both sides. B. p – 8 = 9 p – 8 = p + 0 = 17 p = 17 Identity Property of Zero: p + 0 = p. Check p – 8 = 9 ? 17 – 8 = 9 9 = 9 ?

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Solve. Additional Example 2C: Solving Equations Using Addition and Subtraction Properties Add 11 to both sides. C. 22 = y – = y – = y = y Identity Property of Zero: y + 0 = 0. Check 22 = y – 11 ? 22 = 33 – = 22 ?

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Solve. Try This: Example 2A Subtract 15 from both sides. A n = n = 29 – n = 14 n = 14 Identity Property of Zero: 0 + n = n. Check 15 + n = 29 ? = = 29 ?

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Additional Example 3A + = + = 34 16,550 x + 0 = 16,516 A. Jan took a 34-mile trip in her car, and the odometer showed 16,550 miles at the end of the trip. What was the original odometer reading? Subtract 34 from both sides. x + 34 = 16,550 The original odometer reading was 16,516 miles. odometer reading at the beginning of the trip miles traveled x –34 x = 16,516 Solve: odometer reading at the end of the trip

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Additional Example 3B + = + = n n = 230 B. From 1980 to 2000, the population of a town increased from 895 residents to 1125 residents. What was the increase in population during that 20-year period? Subtract 895 from both sides n = 1125 The increase in population was 230. initial population increase in population 895 –895 n = 230 Solve: population after increase

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1-3 Solving Addition and Subtraction Equations Pre-Algebra Try This: Example 3A + = + = x + 0 = 508 A. Isabelle earned $27 interest and now has a balance of $535 in the bank. What was her balance before interest was added? Subtract 27 from both sides. x + 27 = 535 Isabelle had a balance of $508 before interest was added. balance before interest interest earned x –27 x = 508 Solve: balance after interest

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