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EXAMPLE 1

EXAMPLE 1. Working Backward. One way to solve the equation above to find the number of conch shells you had in your collection at the start is to work backward. EXAMPLE 1. Working Backward.

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EXAMPLE 1

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  1. EXAMPLE 1 Working Backward One way to solve the equation above to find the number of conch shells you had in your collection at the start is to work backward.

  2. EXAMPLE 1 Working Backward One way to solve the equation above to find the number of conch shells you had in your collection at the start is to work backward. After giving away 2 conch shells, you have 5 conch shells. x – 2 = 5

  3. EXAMPLE 1 Working Backward One way to solve the equation above to find the number of conch shells you had in your collection at the start is to work backward. After giving away 2 conch shells, you have 5 conch shells. x – 2 = 5 To find the value x you had before subtracting 2, you can add 2 to undo the subtraction. 5 + 2 = x

  4. EXAMPLE 1 Working Backward ANSWER You had 7 conch shells in your collection at the start.

  5. EXAMPLE 1 Working Backward ANSWER You had 7 conch shells in your collection at the start. Check x – 2 = 5Write the original equation. ? 7 – 2 = 5Substitute 7 for x. Solution checks. 5 = 5

  6. for Example 1 GUIED PRACTICE GUIDED PRACTICE Postcards 1. You mailed 5 postcards and now you have 9 postcards left. How many postcards did you have at the start?

  7. for Example 1 GUIED PRACTICE GUIDED PRACTICE Postcards 1. You mailed 5 postcards and now you have 9 postcards left. How many postcards did you have at the start? ANSWER 14

  8. for Example 1 GUIED PRACTICE GUIDED PRACTICE Isolating the VariableYou can also solve the equation in Example 1 by getting the variable by itself as you did in Lesson 12.2. Use the steps below.

  9. for Example 1 GUIED PRACTICE GUIDED PRACTICE Isolating the VariableYou can also solve the equation in Example 1 by getting the variable by itself as you did in Lesson 12.2. Use the steps below. x – 2 = 5 + 2 + 2 x = 7

  10. for Example 1 GUIED PRACTICE GUIDED PRACTICE Isolating the VariableYou can also solve the equation in Example 1 by getting the variable by itself as you did in Lesson 12.2. Use the steps below. x – 2 = 5 + 2 + 2 x = 7 By adding 2 to each side of the equation, you undo the subtraction while keeping the two sides of the equation equal to each other.

  11. EXAMPLE 2 Solving Subtraction Equations Solve the equation.

  12. EXAMPLE 2 Solving Subtraction Equations Solve the equation. a.14 = n – 6 b.m – 3.1 = 11.95

  13. EXAMPLE 2 Solving Subtraction Equations Solve the equation. a.14 = n – 6 b.m – 3.1 = 11.95 SOLUTION a.In this equation, the variable is on the right side of the equation. 14 = n – 6 + 6+ 6Add 6 to each side. Simplify. Write the original equation. 20 = n

  14. EXAMPLE 2 Solving Subtraction Equations b. m – 3.1 = 11.95 Write the original equation. + 3.1 + 3.1 Add 3.1 to each side. m 15.05 Simplify. =

  15. EXAMPLE 2 Solving Subtraction Equations b. m – 3.1 = 11.95 Write the original equation. + 3.1 + 3.1 Add 3.1 to each side. m 15.05 Simplify. = Check Estimate. Substitute using rounded values: ? 15 – 3 = 12 12 = 12

  16. EXAMPLE 3 Using a Subtraction Equation Elevator You are riding an elevator. You go down 14 floors and exit on the 23rd floor. On what floor did you enter the elevator? SOLUTION Let f represent the number of the floor on which you entered the elevator. f – 14 = 23 Write an equation. + 14 + 14 Add 14 to each side. = 37 Simplify. ANSWER You entered the elevator on the 37th floor.

  17. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Then check the solution.

  18. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Then check the solution. q – 7 = 2 2.

  19. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Then check the solution. ANSWER 9 q – 7 = 2 2.

  20. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Then check the solution. ANSWER 9 q – 7 = 2 2. 25 = s – 17 3.

  21. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Then check the solution. ANSWER 9 q – 7 = 2 2. ANSWER 42 25 = s – 17 3.

  22. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Then check the solution. ANSWER 9 q – 7 = 2 2. ANSWER 42 25 = s – 17 3. 3.2 = r – 2.1 4.

  23. for Examples 2 and 3 GUIDED PRACTICE Solve the equation. Then check the solution. ANSWER 9 q – 7 = 2 2. ANSWER 42 25 = s – 17 3. ANSWER 5.3 3.2 = r – 2.1 4.

  24. for Examples 2 and 3 GUIDED PRACTICE What If? 5. In Example 3, suppose you went down 15 floors and exited on the 29thfloor. On what floor did you enter the elevator?

  25. for Examples 2 and 3 GUIDED PRACTICE What If? 5. In Example 3, suppose you went down 15 floors and exited on the 29thfloor. On what floor did you enter the elevator? ANSWER 44

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