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Transforming Equations: Using Addition and Subtraction for Equation Manipulation

This guide explores the principles of transforming equations through addition and subtraction. The objective is to understand how to modify both sides of an equation without altering its truth. By mastering these techniques, we will solve equations like x - 8 = 17 and -5 = n + 13. Key points include applying the same operations to both sides, understanding the effects of addition and subtraction, and verifying solutions through substitution. This foundational skill is vital for building algebraic proficiency.

iwalani-david
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Transforming Equations: Using Addition and Subtraction for Equation Manipulation

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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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