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2-7 One-Step Equations with Rational Numbers Additional Examples 1A: Solving Equations with Decimals Solve. Evaluating Algebraic Expressions m + 4.6 = 9 m + 4.6 = 9 – 4.6 – 4.6 m = 4.4 Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition. Remember! 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. 2-7 One-Step Equations with Rational Numbers Additional Examples 1B: Solving Equations with Decimals Solve. Evaluating 8.2p = –32.8 Algebraic Expressions 8.2p = –32.8 8.2 8.2 p = –4 Since p is multiplied by 8.2, divide both sides by 8.2. 2-7 One-Step Equations with Rational Numbers Additional Examples 1C: Solving Equations with Decimals Solve. Evaluating Algebraic Expressions x = 15 1.2 x = 1.2 • 15 1.2 • 1.2 x = 18 Since x is divided by 1.2, multiply both sides by 1.2. 2-7 One-Step Equations with Rational Numbers Check It Out! Example 1 Solve. Evaluating Algebraic Expressions A. m + 9.1 = 3 Since 9.1 is added to m + 9.1 = 3 m, subtract 9.1 from –9.1 = –9.1 both sides to undo the m = –6.1 addition. B. 5.5b = 75.9 75.9 5.5 b = 5.5 5.5 b = 13.8 Since b is multiplied by 5.5, divide both sides by 5.5. 2-7 One-Step Equations with Rational Numbers Check It Out! Example 1C Evaluating Algebraic Expressions Solve. y = 90 C. 4.5 y = 4.5 • 90 4.5 • 4.5 y = 405 Since y is divided by 4.5, multiply both sides by 4.5. 2-7 One-Step Equations with Rational Numbers Additional Example 2A: Solving Equations with Fractions Solve. Evaluating n+ n+ 3 2 =– 7 7 Algebraic Expressions 2 2 – = –3 – 2 7 7 7 7 n=– 5 7 2 Since is added to n, subtract 7 2 7 from both sides. 2-7 One-Step Equations with Rational Numbers Additional Example 2B: Solving Equations with Fractions Solve. Evaluating Algebraic Expressions 1 2 = 6 3 1 1 1 Since is subtracted from y, add 2 1 6 y– + = + 1 6 6 3 6 6 to both sides. 4 1 y= + Find a common denominator, 6. 6 6 5 y= 6 y– 2-7 One-Step Equations with Rational Numbers Additional Example 2C: Solving Equations with Fractions Solve. Evaluating 5 5x = 8 6 5x 5 5 5 ÷ = ÷ 6 8 6 6 1 1 1 3 6 5 5 6 x• 5 = 8 • 6 5 4 1 1 1 3 x = 4 Algebraic Expressions 5 Since x is multiplied by , 5 6 divide both sides by 6 . Multiply by the reciprocal. Simplify. 2-7 One-Step Equations with Rational Numbers Check It Out! Example 2A Solve. Evaluating Algebraic Expressions 5 1 n+ =– 9 9 1 1 5 1 n+ – =– – 9 9 9 9 n=– 6 9 2 n=– 3 1 Since is added to n, subtract 9 1 9 from both sides. Simplify. 2-7 One-Step Equations with Rational Numbers Check It Out! Example 2B Solve. Evaluating Algebraic Expressions y– 1 = 3 2 4 1 1 1 Since is subtracted from y, add 2 y– + = 3 +1 1 2 2 4 2 2 to both sides. 3 2 y= + Find a common denominator, 4. 4 4 5 y= 4 1 Simplify. y= 1 4 2-7 One-Step Equations with Rational Numbers Check It Out! Example 2C Solve. Evaluating Algebraic Expressions 3 3x = 4 8 3x 3 3 3 ÷ = ÷ 8 4 8 8 1 18 1 3 3 82 x• 3 = 4 • 8 3 1 1 1 1 x=2 3 Since x is multiplied by , 3 8 divide both sides by 8 . Multiply by the reciprocal. Simplify. 2-7 One-Step Equations with Rational Numbers Additional Example 3: Solving Word Problems Using Equations Evaluating Algebraic Expressions 1 Janice has saved $21.40. This is 3 of what she needs to save to buy a new piece of software. What is the total amount that Janice needs to save? Write an equation: Amount Needed a 1/3 = 1 3 = Amount Saved $21.40 2-7 One-Step Equations with Rational Numbers Additional Example 3 Continued Evaluating Algebraic Expressions 1 1 ax1 ÷ = 21.40 ÷ 3 3 3 1 Since a is multiplied by , 1 3 divide both sides by 3 . 1 3 3 3 1 = 21.40 1 Multiply by the reciprocal. a a = 64.20 Simplify. Janice needs to save $64.20. 2-7 One-Step Equations with Rational Numbers Check It Out! Example 3 2 Rick’s car holds 3 the amount of gasoline as his Evaluating Algebraic Expressions wife’s van. If the car’s gas tank can hold 24 gallons of gasoline, how much gasoline can the tank in the minivan hold? Write an equation: Capacity of minivan’s tank g • 2/3 = Capacity of car’s tank • 2 3 = 24 2-7 One-Step Equations with Rational Numbers Check It Out! Example 3 Continued 2 Evaluating Algebraic Expressions Since g is multiplied by , 2 2 2 g 3 ÷ 3 = 24 ÷ 3 2 3 3 g 3 2 = 24 2 2 3 divide both sides by 3 . Multiply by the reciprocal. g = 72 2 g = 36 Simplify. The minivan can hold 36 gallons of gas. 2-7 One-Step Equations with Rational Numbers 5 j = –15 12 Solve. x =Algebraic 41.1 Evaluating Expressions 3 2 1. x – 23.3 = 17.8 2. j + = –14 4 3 Lesson Quiz 3 3. 9y = y= 1 5 15 d = 2 3 d = 91 4. 4 2 8 2 5. Tamara can mow 5 acre in one hour. If her yard is 2 acres, how many hours will it take her to mow the entire yard? 5 hours