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Warm Up

Preview. Warm Up. California Standards. Lesson Presentation. 1. 1. 5. 1. 1. 16. Warm Up Add or subtract. 5 10. 7 10. 1. +. 3 8. 5 16. 2. 2 – 1. 3. 4.8 + 3.6. 8.4. 2.35. 4. 2.4 – 0.05. California Standards.

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Warm Up

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  1. Preview Warm Up California Standards Lesson Presentation

  2. 1 1 5 1 1 16 Warm Up Add or subtract. 5 10 7 10 1. + 3 8 5 16 2. 2 – 1 3. 4.8 + 3.6 8.4 2.35 4. 2.4 – 0.05

  3. California Standards AF4.0 Students solve simple linear equations and inequalities over the rational numbers.

  4. – 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 m + 4.6 = 9 Since 4.6 is added to m, subtract 4.6 from both sides to undo the addition.

  5. –32.8 8.2 8.2p 8.2 = p = –4 Additional Examples 1B: Solving Equations with Decimals Solve. 8.2p = –32.8 Since p is multiplied by 8.2, divide both sides by 8.2.

  6. x 1.2 = 15 x 1.2 = 1.2 •15 1.2 • Additional Examples 1C: Solving Equations with Decimals Solve. Since x is divided by 1.2, multiply both sides by 1.2. x = 18

  7. 75.9 5.5 5.55.5 b = –9.1 –9.1 = 13.8 b = = –6.1 m Check It Out! Example 1 Solve. A. m + 9.1 = 3 Since 9.1 is added to m, subtract 9.1 from both sides to undo the addition. m + 9.1 = 3 B. 5.5b = 75.9 Since b is multiplied by 5.5, divide both sides by 5.5.

  8. y 4.5 = 4.5 •90 4.5 • Check It Out! Example 1C Solve. y 4.5 = 90 C. Since y is divided by 4.5, multiply both sides by 4.5. y = 405

  9. 3 7 2 7 n + = – 5 7 n = – 2 7 2 7 3 7 27 n + – = – – Since is added to n, subtract from both sides. 27 2 7 Additional Example 2A: Solving Equations with Fractions Solve.

  10. Since is subtracted from y, add to both sides. 1 6 1 6 2 3 1 6 1 6 1 6 y – = + + 5 6 y = 4 6 1 6 y = + Additional Example 2B: Solving Equations with Fractions Solve. 1 6 2 3 y – = Find a common denominator, 6.

  11. Since x is multiplied by , divide both sides by . 5 6 5 8 5 6 5 6 x 5 6 5 6 ÷ = ÷ 6 5 5 8 5 6 6 5 • = x • 3 4 = x Additional Example 2C: Solving Equations with Fractions Solve. 5 8 5 6 x = 1 1 1 3 Multiply by the reciprocal. Simplify. 4 1 1 1

  12. 6 9 2 3 n = – n = – 1 9 1 9 5 9 19 n + – = – – Since is added to n, subtract from both sides. 19 1 9 Check It Out! Example 2A Solve. 5 9 1 9 n + = – Simplify.

  13. 1 2 3 4 y – = Since is subtracted from y, add to both sides. 1 2 1 2 3 4 1 2 1 2 1 2 y – = + + 5 4 y = 3 4 2 4 y = + 1 4 y = 1 Check It Out! Example 2B Solve. Find a common denominator, 4. Simplify.

  14. Since x is multiplied by , divide both sides by . 3 8 3 4 3 8 3 8 x 3 8 3 8 ÷ = ÷ 8 3 3 4 3 8 8 3 • = x • Check It Out! Example 2C Solve. 3 4 3 8 x = 1 1 1 2 Multiply by the reciprocal. Simplify. 1 1 1 1 x = 2

  15. 1 3 1 3 Additional Example 3: Solving Word Problems Using Equations Janice has saved $21.40. 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? Write an equation: Amount Saved Amount Needed  1/3 = = $21.40  a

  16. a x ÷ = 21.40 ÷ 1 3 3 1 3 1  a  = 21.40 Since a is multiplied by , divide both sides by . 1 3 1 3 1 3 1 3 1 3 a = 64.20 Additional Example 3 Continued Multiply by the reciprocal. Simplify. Janice needs to save $64.20.

  17. 2 3 Rick’s car holds the amount of gasoline as his 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? 2 3 24 Check It Out! Example 3 Write an equation: Capacity of car’s tank Capacity of minivan’s tank 2/3 • = g • =

  18. g  ÷ = 24 ÷ 2 3 3 2 3 2  g  = 24 Since g is multiplied by , divide both sides by . 2 3 2 3 2 3 2 3 2 3 722 g = g = 36 Check It Out! Example 3 Continued Multiply by the reciprocal. Simplify. The minivan can hold 36 gallons of gas.

  19. 3 4 2 3 3 8 d 3 5 5 12 = 2 j = –15 4 1 y = 2 5 15 1 d = 9 2 Lesson Quiz Solve. x = 41.1 1.x – 23.3 = 17.8 2.j + = –14 4. 3. 9y = 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

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