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Notes 55

Notes 55. Solving Equations With Rational Numbers. – 4.6. =. – 4.6. =. 4.4 . m. 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.

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Notes 55

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  1. Notes 55 Solving Equations With Rational Numbers

  2. – 4.6 = –4.6 = 4.4 m 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. Additional Examples 1A: Solving Equations with Decimals Solve. m + 4.6 = 9 Use the Subtraction Property of Equality. Subtract 4.6 from both sides. m + 4.6 = 9

  3. –32.8 8.2 8.2p 8.2 = p = –4 Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 Use the Division Property of Equality. Divide both sides by 8.2.

  4. x 1.2 = 15 x 1.2 = 1.2 •15 1.2 • Additional Examples 1C: Solving Equations with Decimals Solve. Use the Multiplication Property of Equality. Multiply both sides by 1.2. x = 18

  5. Check It Out: Example 1A and 1B Solve each equation. A. m + 9.1 = 3 B. –3.1p = 15.5

  6. 2 7 27 2 7 3 7 27 n – + = – – Subtract from both sides. 5 7 n = – Additional Example 2A: Solving Equations with Fractions Solve. 3 7 2 7 n + = –

  7. 1 6 1 6 2 3 1 6 1 6 y – + + = Add to both sides. 4 6 1 6 y = + 5 6 y = Additional Example 2B: Solving Equations with Fractions Solve. 1 6 2 3 y – = Find a common denominator, 6.

  8. 5 6 5 6 5 8 5 6 5 6 Divide both sides by . x ÷ = ÷ 5 8 6 5 5 6 6 5 = • x • 3 4 = x Additional Example 2C: Solving Equations with Fractions Solve. 5 8 5 6 x = 3 Multiply by the reciprocal. 4 Simplify.

  9. Check It Out: Example 2A Solve each equation. 5 8 1 3 m – =

  10. Check It Out: Example 2B Solve each equation. 3 8 6 19 x =

  11. Mr. Rios wants to prepare a dessert, but only has 2 tablespoons of sugar. If each serving of the dessert has tablespoon of sugar, how many servings can he make for the party? 2 3 2 3 2 3 2 3 = 2  s Additional Example 3: Solving Word Problems Using Equations Write an equation: Amount needed for each dessert Amount of sugar Total servings  =

  12. 2 3 2 3 2 3 s = 2  2 3 3 2 2 3 2 3 3 2 2 3 2 3 2 3 s s  ÷  = 2  ÷ = 2  Divide both sides by . 8 3 3 2  = s 24 6 , or 4 s = Additional Example 3 Continued Now solve the equation. Multiply both sides by the reciprocal. Simplify. Mr. Rios can make 4 servings.

  13. 3 5 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 16 gallons of gasoline, how much gasoline can the tank in the minivan hold? 1 2 Check It Out: Example 3

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