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3.1 Transforming Equations

3.1 Transforming Equations. Objective: Changing Equations with Addition and Subtraction 2 = 2. 3.1 Transforming Equations. Objective: Changing Equations with Addition and Subtraction 2 + 3 = 2 + 3 When you add 3 to BOTH sides it is still TRUE. 3.1 Transforming Equations.

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3.1 Transforming Equations

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  1. 3.1 Transforming Equations • Objective: Changing Equations with Addition and Subtraction • 2 = 2

  2. 3.1 Transforming Equations • Objective: Changing Equations with Addition and Subtraction • 2 + 3 = 2 + 3 • When you add 3 to BOTH sides it is still TRUE

  3. 3.1 Transforming Equations • Objective: Changing Equations with Addition and Subtraction • 2 + 3 = 2 + 3 • When you add 3 to BOTH sides it is still TRUE 5 = 5. • What if you subtract a number, any number???

  4. 3.1 Transforming Equations • Objective: Changing Equations with Addition and Subtraction • 2 + 3 = 2 + 3 • When you add 3 to BOTH sides it is still TRUE 5 = 5. • What if you subtract a number, any number??? • 2 – 37 = 2 - 37

  5. 3.1 Transforming Equations • Objective: Changing Equations with Addition and Subtraction • 2 + 3 = 2 + 3 • When you add 3 to BOTH sides it is still TRUE 5 = 5. • What if you subtract a number, any number??? • 2 – 37 = 2 – 37 • - 35 = -35 STILL TRUE!!!!

  6. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation.

  7. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Also adding undoes subtraction and • Subtraction undoes adding. • Example 1: Solve x – 8 = 17

  8. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Example 1: Solve x – 8 = 17 • I need x by itself, on one side and the numbers on the other.

  9. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Example 1: Solve x – 8 = 17 • I need x by itself, on one side and the numbers on the other. • What operation is with the x side?

  10. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Example 1: Solve x – 8 = 17 • I need x by itself, on one side and the numbers on the other. • What operation is with the x side? Subtraction

  11. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Example 1: Solve x – 8 = 17 • I need x by itself, on one side and the numbers on the other. • What operation is with the x side? Subtraction, to undo subtraction – ADD.

  12. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Example 1: Solve x – 8 = 17 • + 8 = + 8 • IF you do something to one side, DO it to the other so you do not change the problem.

  13. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Example 1: Solve x – 8 = 17 • + 8 = + 8 • x = 25 • Check answer by substituting back into original problem. 25 - 8 = 17

  14. 3.1 Transforming Equations • Remember: Add or Subtract ANY number to BOTH, BOTH Sides does not change the equation. • Example 1: Solve x – 8 = 17 • + 8 = + 8 • x = 25 • Check answer by substituting back into original problem. 25 - 8 = 17 • 17 = 17 

  15. 3.1 Transforming Equations • Example 2: Solve -5 = n + 13

  16. 3.1 Transforming Equations • Example 2: Solve -5 = n + 13 • I want n – 13 = - 13 • By itself so make • the number 0

  17. 3.1 Transforming Equations • Example 2: Solve -5 = n + 13 • – 13 = – 13 • -18 = n

  18. 3.1 Transforming Equations • Example 2: Solve -5 = n + 13 • – 13 = – 13 • -18 = n • CHECK: -5 = -18 + 13

  19. 3.1 Transforming Equations • Example 2: Solve -5 = n + 13 • – 13 = – 13 • -18 = n • CHECK: -5 = -18 + 13 • -5 = -5 

  20. 3.1 Transforming Equations • Example 3: Solve (a – 3) + 19 = 125 • Need to simplify FIRST, get rid of ( ): • a + (- 3) + 19 = 125

  21. 3.1 Transforming Equations • Example 3: Solve (a – 3) + 19 = 125 • Need to simplify FIRST: • a + (- 3) + 19 = 125 • a + 16 = 125

  22. 3.1 Transforming Equations • Example 3: Solve (a – 3) + 19 = 125 • Need to simplify FIRST: • (a – 3) + 19 = 125 • a + (- 3) + 19 = 125 • a + 16 = 125

  23. 3.1 Transforming Equations • Example 3: Solve (a – 3) + 19 = 125 • Need to simplify FIRST: • (a – 3) + 19 = 125 • a + (- 3) + 19 = 125 • a + 16 = 125 • - 16 = -16

  24. 3.1 Transforming Equations • Example 3: Solve (a – 3) + 19 = 125 • Need to simplify FIRST: • (a – 3) + 19 = 125 • a + (- 3) + 19 = 125 • a + 16 = 125 • - 16 = -16 • a = 109 • CHECK (109 – 3) + 19 = 125

  25. 3.1 Transforming Equations • Example 3: Solve (a – 3) + 19 = 125 • Need to simplify FIRST: • (a – 3) + 19 = 125 • a + (- 3) + 19 = 125 • a + 16 = 125 • - 16 = -16 • a = 109 • CHECK (109 – 3) + 19 = 125 • 106 +19 =125

  26. 3.1 Transforming Equations • Example 3: Solve (a – 3) + 19 = 125 • Need to simplify FIRST: • (a – 3) + 19 = 125 • a + (- 3) + 19 = 125 • a + 16 = 125 • - 16 = -16 • a = 109 • CHECK (109 – 3) + 19 = 125 • 106 +19 =125 • 125 = 125√

  27. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w)

  28. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 – (4 + (-W)) • 1 = -2 +(-4) + w

  29. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 +(-4) + w • 1 = -6 + w

  30. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 +(-4) + w • 1 = -6 + w • + 6 = + 6

  31. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 +(-4) + w • 1 = -6 + w • + 6 = + 6 • 7 = w

  32. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 +(-4) + w • 1 = -6 + w • + 6 = + 6 • 7 = w • CHECK 1 = -2 – (4 – 7)

  33. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 +(-4) + w • 1 = -6 + w • +6 = +6 • 7 = w • CHECK 1 = -2 – (4 – 7) • 1 = -2 – (-3)

  34. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 +(-4) + w • 1 = -6 + w • +6 = + 6 • 7 = w • CHECK 1 = -2 – (4 – 7) • 1 = -2 – (-3) • 1 = -2 + 3

  35. 3.1 Transforming Equations • Example 4: Solve 1 = -2 – (4 – w) • Need to simplify FIRST: • 1 = -2 +(-4) + w • 1 = -6 + w • +6 = + 6 • 7 = w • CHECK 1 = -2 – (4 – 7) • 1 = -2 – (-3) • 1 = -2 + 3 • 1 = 1

  36. 3.1 Transforming Equations • Oral : P 97 • Homework P. 97 3 – 45 every third.

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