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Mastering Two-Step Equations: Techniques and Strategies

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cosmo
19 diapositives · 350 Views · Jul 27, 2014

This guide focuses on solving two-step equations by using inverse operations in reverse order. It covers essential examples, such as solving equations of the form ax + b = c, and emphasizes the importance of checking your answers. Additionally, it provides a framework for tackling word problems systematically, including defining variables, planning methods, and verifying solutions. Real-life examples illustrate the application of these techniques, making the concepts accessible and practical for learners.

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  1. Algebra 1 Section 2.5

  2. Solving Two-Step Equations The operations done to a variable must be undone using inverse operations in reverse order.

  3. Example 1 Solve 2x + 6 = 21. 2x + 6 = 21 2x + 6 – 6 = 21 – 6 2x= 15

  4. Example 1 2x = 15 2x 15 = 2 2 15 x = 2 Did you check your answer?

  5. Example 2 a Solve – 3.6 = -4.4. 1.5 a – 3.6 + 3.6 = -4.4 + 3.6 1.5 a = -0.8 1.5

  6. Example 2 a ( ) 1.5 = 1.5(-0.8) 1.5 -1.2 – 3.6 = -0.8 – 3.6 = -4.4 1.5 a a = -1.2 = -0.8 1.5

  7. Solving Equations of the Form ax + b = c Undo the addition or subtraction of the constant term. Undo the multiplication or division done to the variable.

  8. Example 3 x Solve – 7 = 2. 3 x x – 7 + 7 = 2 + 7 = 9 3 3

  9. Example 3 x ( ) x 3 = 3(9) = 9 3 3 x = 27

  10. Solving Word Problems Step 1: Read the Problem Draw a picture, if possible Assign a variable to the main unknown

  11. Solving Word Problems Step 2: Plan a Method of Attack Make a table, if possible Translate word phrases into expressions using the variable

  12. Solving Word Problems Step 3: Solve an Equation Write an equation Solve the equation

  13. Solving Word Problems Step 4: Check your Solution Have I answered all of the questions in the problem? What do the numbers represent? Are the answers reasonable?

  14. Example 4 Ninety-seven is twenty-four less than four times a number. 97 = 4x – 24

  15. Example 5 How many quarters must be removed from $2.64 to leave a total of $1.89? q = number of quarters 0.25q = value of the quarters 2.64 – 0.25q = 1.89

  16. Example 6 The grain elevator weighed Mr. Young’s truck at 17,760 lb before he dumped his wheat. The weight of the empty truck is 6180 lb. If the wheat weighed 60 lb/bu, how many bushels of wheat did he deliver to the elevator?

  17. Example 6 The grain elevator weighed Mr. Young’s truck at 17,760 lb before he dumped his wheat. The weight of the empty truck is 6180 lb. If the wheat weighed 60 lb/bu, how many bushels of wheat did he deliver to the elevator? b = bushels of wheat 60b = the weight of the wheat

  18. Example 6 The grain elevator weighed Mr. Young’s truck at 17,760 lb before he dumped his wheat. The weight of the empty truck is 6180 lb. If the wheat weighed 60 lb/bu, how many bushels of wheat did he deliver to the elevator? 60b + 6180 = 17,760

  19. Homework: pp. 72-74