Warm Up California Standards Lesson Presentation Preview
Warm Up Solve. 1.   x  + 12 = 35 2.  8 x  = 120 3.   = 7 4.  –34 =  y  + 56 x  = 23 x  = 15 y  = 63 y  = –90 y 9
AF4.1  Solve two-step linear equations  and inequalities  in one variable over the rational numbers,  interpret the soluti...
Recall that two-step equations contain two operations, and therefore, require two inverse operations to solve. Before solv...
The mechanic’s bill to repair Mr. Wong’s car was $653.05. The mechanic charges $45.50 an hour for labor, and the parts tha...
Additional Example 1 Continued The  answer  is the number of hours the mechanic worked on the car. List the important info...
Think:  First the variable is multiplied by 45.50, and then 443.75 is added to the result. Work backward to solve the equa...
653.05 =  443.75 + 45.50 h – 443.75   –443.75 209.30 =   45.50 h 4.6 =  h The mechanic worked for 4.6 hours on Mr. Wong’s ...
You can use a table to decide whether your answer is reasonable. Additional Example 1 Continued 4.6 hours is a reasonable ...
The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used ...
Check It Out!  Example 1 Continued The  answer  is the number of hours the mechanic worked on your car. List the important...
Think:  First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. ...
850 =  275 + 35 h – 275   –275 575 =   35 h 16.4     h The mechanic worked for about 16.4 hours on your car. Check It Out...
Check It Out!  Example 1 Continued You can use a table to decide whether your answer is reasonable. 16.4 hours is a reason...
Additional Example 2A: Solving Two-Step Equations Solve  + 7 = 22. Since n is divided by 3, multiply both sides by 3. n  =...
Additional Example 2B: Solving Two-Step Equations  Solve  = 9. y  – 4 = 27 + 4   + 4 Since 4 is subtracted from y,  add 4 ...
Check It Out!  Example 2A Solve  + 8 = 18. Since n is divided by 4, multiply both sides by 4. n  = 40 Method 1:  Use fract...
Check It Out!  Example 2B Solve  = 7. y  – 7 = 14 + 7   + 7 Since 7 is subtracted from y,  add 7 to both sides to undo  th...
Solve. 1.  –  x  – 3 = 10 2.  7 y  + 25.68 = –26.12 3.  –8.3 = –3.5 x  + 13.4 4.  = 3.1 5.  The cost for a new cell phone ...
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Chapter2.8

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Chapter2.8

  1. 1. Warm Up California Standards Lesson Presentation Preview
  2. 2. Warm Up Solve. 1. x + 12 = 35 2. 8 x = 120 3. = 7 4. –34 = y + 56 x = 23 x = 15 y = 63 y = –90 y 9
  3. 3. AF4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the solution or solutions in the context from which they arose, and verify the reasonableness of the results. California Standards
  4. 4. Recall that two-step equations contain two operations, and therefore, require two inverse operations to solve. Before solving, ask yourself, “What is being done to the variable, and in what order?” One method to solve the equation is to work backward to undo the operations.
  5. 5. The mechanic’s bill to repair Mr. Wong’s car was $653.05. The mechanic charges $45.50 an hour for labor, and the parts that were used cost $443.75. How many hours did the mechanic work on the car? Additional Example 1: Problem Solving Application
  6. 6. Additional Example 1 Continued The answer is the number of hours the mechanic worked on the car. List the important information: Let h represent the hours the mechanic worked. <ul><li>The parts cost $443.75. </li></ul><ul><li>The labor cost $45.50 per hour. </li></ul><ul><li>The total bill was $653.05. </li></ul>Total bill = Parts + Labor 653.05 = 443.75 + 45.50 h 1 Understand the Problem
  7. 7. Think: First the variable is multiplied by 45.50, and then 443.75 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 443.75 from both sides of the equation, and then divide both sides of the new equation by 45.50. Additional Example 1 Continued 2 Make a Plan
  8. 8. 653.05 = 443.75 + 45.50 h – 443.75 –443.75 209.30 = 45.50 h 4.6 = h The mechanic worked for 4.6 hours on Mr. Wong’s car. Additional Example 1 Continued Since h is multiplied by 45.50, divide both sides by 45.50. Since 443.75 is added to both sides, subtract 443.75 from both sides. Solve 3 209.30 45.50 h 45.50 45.50 =
  9. 9. You can use a table to decide whether your answer is reasonable. Additional Example 1 Continued 4.6 hours is a reasonable answer. Look Back 4 $671.25 $443.75 $227.50 5 $625.75 $443.75 $182.00 4 $580.25 $443.75 $136.50 3 $534.75 $443.75 $91.00 2 $489.25 $443.75 $45.50 1 Total Cost Parts Labor Hours
  10. 10. The mechanic’s bill to repair your car was $850. The mechanic charges $35 an hour for labor, and the parts that were used cost $275. How many hours did the mechanic work on your car? Check It Out! Example 1
  11. 11. Check It Out! Example 1 Continued The answer is the number of hours the mechanic worked on your car. List the important information: Let h represent the hours the mechanic worked. <ul><li>The parts cost $275. </li></ul><ul><li>The labor cost $35 per hour. </li></ul><ul><li>The total bill was $850. </li></ul>Total bill = Parts + Labor 850 = 275 + 35 h 1 Understand the Problem
  12. 12. Think: First the variable is multiplied by 35, and then 275 is added to the result. Work backward to solve the equation. Undo the operations in reverse order: First subtract 275 from both sides of the equation, and then divide both sides of the new equation by 35. Check It Out! Example 1 Continued 2 Make a Plan
  13. 13. 850 = 275 + 35 h – 275 –275 575 = 35 h 16.4  h The mechanic worked for about 16.4 hours on your car. Check It Out! Example 1 Continued Since h is multiplied by 35, divide both sides by 35. Since 275 is added to both sides, subtract 275 from both sides. Solve 3 575 35 h 35 35 =
  14. 14. Check It Out! Example 1 Continued You can use a table to decide whether your answer is reasonable. 16.4 hours is a reasonable answer. Look Back 4 $870 $275 $595 17 $835 $275 $560 16 $800 $275 $525 15 $765 $275 $490 14 $730 $275 $455 13 Total Cost Parts Labor Hours
  15. 15. Additional Example 2A: Solving Two-Step Equations Solve + 7 = 22. Since n is divided by 3, multiply both sides by 3. n = 45 Method 1: Use fraction operations. n 3 + 7 – 7 = 22 – 7 n 3 3  = 3  15 n 3 + 7 = 22 n 3 Since 7 is added to , subtract 7 from both sides to undo the addition. n3 = 15 n 3
  16. 16. Additional Example 2B: Solving Two-Step Equations Solve = 9. y – 4 = 27 + 4 + 4 Since 4 is subtracted from y, add 4 to both sides to undo the subtraction. y = 31 Multiply both sides by the denominator. Method 2: Multiply both sides of the equation by the denominator. y – 4 3 = 9 y – 4 3 = 9 y – 4 3 (3) (3)
  17. 17. Check It Out! Example 2A Solve + 8 = 18. Since n is divided by 4, multiply both sides by 4. n = 40 Method 1: Use fraction operations. n 4 + 8 – 8 = 18 – 8 n 4 4  = 4  10 n 4 + 8 = 18 n 4 Since 8 is added to , subtract 8 from both sides to undo the addition. n4 = 10 n 4
  18. 18. Check It Out! Example 2B Solve = 7. y – 7 = 14 + 7 + 7 Since 7 is subtracted from y, add 7 to both sides to undo the subtraction. y = 21 Multiply both sides by the denominator. Method 2: Multiply both sides of the equation by the denominator. y – 7 2 = 7 y – 7 2 = 7 y – 7 2 (2) (2)
  19. 19. Solve. 1. – x – 3 = 10 2. 7 y + 25.68 = –26.12 3. –8.3 = –3.5 x + 13.4 4. = 3.1 5. The cost for a new cell phone plan is $39 per month plus a one-time start-up fee of $78. If you are charged $1032.96, how many months will the contract last? Lesson Quiz y = –7.4 x = –117 x = 6.2 y = 29.1 24 months 1 9 y + 5 11
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