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Chapter 7 - Equations

Chapter 7 - Equations. 7.6 - Solving Equations with Fractions and Decimals. – 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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Chapter 7 - Equations

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  1. Chapter 7 - Equations 7.6 - Solving Equations with Fractions and Decimals

  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. Example : Solving Equations with Decimals. Solve. m + 4.6 = 9 A. m + 4.6 = 9 Subtract 4.6 from both sides.

  3. –32.8 8.2 8.2p 8.2 = p = –4 Additional Example: Solving Equations with Decimals Solve. 8.2p = –32.8 B. Divide both sides by 8.2

  4. x 1.2 = 1.2 •15 1.2 • Additional Example: Solving Equations with Decimals Solve. x 1.2 C. = 15 Multiply both sides by 1.2 x = 18

  5. 75.9 5.5 5.55.5 b = –9.1 –9.1 = 13.8 b = = –6.1 m Try This Solve. A. m + 9.1 = 3 m + 9.1 = 3 Subtract 9.1 from both sides. B. 5.5b = 75.9 Divide both sides by 5.5

  6. y 4.5 = 4.5 •90 4.5 • Try This Solve. y 4.5 = 90 C. Multiply both sides by 4.5 y = 405

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

  8. 1 6 Add to both sides. 1 6 1 6 2 3 1 6 y – + + = 4 6 1 6 y = + 5 6 y = Solving Equations with Fractions Solve. 1 6 2 3 B. y – = Find a common denominator; 6. Simplify.

  9. 6 5 Multiply both sides by . 5 8 6 5 5 6 6 5 = • x • 3 4 = x Solving Equations with Fractions Solve. 5 8 5 6 C. x = 3 4 Simplify.

  10. 1 9 Subtract from both sides. 19 6 9 1 9 5 9 19 2 3 n – + = – – Simplify – . n = – Try This Solve. 5 9 1 9 A. n + = –

  11. 1 2 Add to both sides. 1 2 1 2 3 4 1 2 y – + + = 3 4 2 4 y = + 1 4 y = 1 Try This: Solve. 1 2 3 4 B. – = y Find a common denominator; 4. Simplify.

  12. 6 19 3 8 x = 6 19 8 3 3 8 8 3 x = • • 8 3 Multiply both sides by . 16 19 = x Try This: Solve. 6 19 3 8 x C. = 2 1 Simplify.

  13. 1 2 Mr. Ayaz wants to prepare a casserole that requires 2 cups of milk. If he makes the casserole, he will have only cup of milk left for his breakfast cereal. How much milk does Mr. Ayaz have? 3 4 2(2)+1 2 1 2 5 2 = = 2 5 2 3 4 Solving Word Problems Using Equations Convert fractions: Write an equation: Milk for cereal Original amount of milk Milk for casserole – = – = c

  14. 5 2 5 2 3 4 5 2 5 2 c – Add to both sides. + = + 3 4 10 4 c = + 1 4 13 4 , or 3 c = 1 4 Mr. Rios has 3 cups of milk. Solving Word Problems Using Equations Now solve the equation. 5 2 3 4 c = – Find a common denominator, 4. Simplify.

  15. 2 3 Rick’s car holds the amount of gasoline as his wife’s van. If the car’s gas tank can hold 15.5 gallons of gasoline, how much gasoline can the tank in the minivan hold? 15(2)+1 31 1 15.5 = 15 = = 2 2 2 2 3 31 2 Try This: Convert decimal to a fraction: Write an equation: Capacity of car’s tank Van’s gas tank Ratio of car’s tank to van’s tank • = g • =

  16. 3 2 3 2 2 3 31 2 Multiply both sides by . g = • • • 3 2 93 4 g = 1 4 g = 23 1 4 The van’s gas tank holds 23 gallons of gasoline. Try This: Now solve the equation. 31 2 2 3 g = • Simplify.

  17. 5 12 j = –15 1 y = 15 1 d = 9 2 Extra Questions Solve. 1.x – 23.3 = 17.8 x = 41.1 3 4 2 3 2.j + = –14 3 5 3. 9y = 3 8 d = 2 4. 4

  18. 1 3 Word Problem Tamara had 6 bags of mulch for her garden. Each bag contained 8 lb of mulch. What was the total weight of the mulch? 5. 50 lb

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