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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers m = 9 Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition. Once you have solved an equation, it is a good idea to check your answer. To check your answer, substitute your answer for the variable in the original equation. Remember! Additional Examples 1A: Solving Equations with Decimals Solve. 4.4 m = – 4.6

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 8.2p = –32.8 –4 p = Since p is multiplied by 8.2, divide both sides by 8.2. – p 8.2 = Additional Examples 1B: Solving Equations with Decimals Solve.

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Additional Examples 1C: Solving Equations with Decimals x = 18 Since x is divided by 1.2, multiply both sides by 1.2. = 15 x 1.2 = Solve.

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers m = 3 Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition. Check It Out! Example 1 –6.1 m = –9.1 = Solve. A. B. 5.5b = = b 13.8 b = Since b is multiplied by 5.5, divide both sides by 5.5.

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers = 90 Check It Out! Example 1C y = 405 Since y is divided by 4.5, multiply both sides by 4.5. y 4.5 = Solve. C.

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Additional Example 2A: Solving Equations with Fractions = – 3737 n n + – = – – n = – 5757 Solve Since is added to n, subtract from both sides. 2727

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 1616 = 2323 y – Additional Example 2B: Solving Equations with Fractions Find a common denominator, 6. =y = y – Solve. Since is subtracted from y, add to both sides =y 5656

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 5656 = 5858 x = 5858 x Multiply by the reciprocal. Simplify. Additional Example 2C: Solving Equations with Fractions x = Solve. Since x is multiplied by, divide both sides by ÷ = ÷ 5858 x

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers 1919 = – 5959 n + Check It Out! Example 2A n = – 2323 Simplify. Solve. n + – = – – n = – Since is added to n, subtract from both sides. 1919

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Check It Out! Example 2B y = Solve. Simplify. =y – Find a common denominator, 4. =y = y – Since is subtracted from y, add to both sides =y 5454

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Check It Out! Example 2C Solve = 3434 x = 3434 x Multiply by the reciprocal. Simplify. x = Since x is multiplied by, divide both sides by ÷ = ÷ 3434 x

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Write an equation: Amount Needed1/3 Amount Saved Additional Example 3: Solving Word Problems Using Equations = Janice has saved $ This is of what she needs to save to buy a new piece of software. What is the total amount that Janice needs to save? 1313 a 1313 = $21.40

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Additional Example 3 Continued Janice needs to save $ = a a = Multiply by the reciprocal. Simplify. Since a is multiplied by, divide both sides by = ÷ a x ÷

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Write an equation: Capacity of minivans tank 2/3 Capacity of cars tank = Check It Out! Example 3 g Ricks car holds the amount of gasoline as his wifes van. If the cars gas tank can hold 24 gallons of gasoline, how much gasoline can the tank in the minivan hold? 2323 =

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Check It Out! Example 3 Continued The minivan can hold 36 gallons of gas = 24 g g = 36 Multiply by the reciprocal. Simplify. Since g is multiplied by, divide both sides by = 24 ÷ g ÷ g = 72 2

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Evaluating Algebraic Expressions 2-7 One-Step Equations with Rational Numbers Lesson Quiz Solve. 1. x – 23.3 = j + = – y = y = x = 41.1 j = – d 4 = d = 9 Tamara can mow acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5. 5 hours 2525

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