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Mastering Equations: Variables on Both Sides

Learn to solve equations with variables on both sides effectively with multiple steps for accurate solutions. Master determining when equations have one solution, no solution, or all real number solutions. Get ready with graph paper for Chapter 4!

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Mastering Equations: Variables on Both Sides

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  1. Lesson 3-5:Solving Equations with the Variable on Each Side

  2. Objectives • I can solve equations with variables on both sides using multiple steps. • I can determine when an equation has one solution, no solutions, and all real numbers for solutions.

  3. You will need graph paper at the beginning of Chapter 4!!!!

  4. Example 1 Solve: -2 + 10p = 8p – 1 – 8p – 8p -2 + 2p = -1

  5. Example 1 Solve: -2 + 10p = 8p – 1 – 8p – 8p -2 + 2p = -1 +2 +2 2p = 1

  6. Example 1 Solve: -2 + 10p = 8p – 1 – 8p – 8p -2 + 2p = -1 +2 +2 2p = 1 p = ½

  7. Example 2 Solve: 2(w – 3) + 5 = 3(w – 1)

  8. Example 2 Solve: 2(w – 3) + 5 = 3(w – 1) 2w – 6 + 5 = 3w – 3

  9. Example 2 Solve: 2(w – 3) + 5 = 3(w – 1) 2w – 6 + 5 = 3w – 3 2w - 1 = 3w – 3

  10. Example 2 Solve: 2(w – 3) + 5 = 3(w – 1) 2w - 6 + 5 = 3w – 3 2w – 1 = 3w – 3 – 2w – 2w

  11. Example 2 Solve: 2(w – 3) + 5 = 3(w – 1) 2w - 6 + 5 = 3w – 3 2w – 1 = 3w – 3 – 2w – 2w -1 = w – 3

  12. Example 2 Solve: 2(w – 3) + 5 = 3(w – 1) 2w - 6 + 5 = 3w – 3 2w - 1 = 3w – 3 – 2w – 2w -1 = w – 3 + 3 + 3

  13. Example 2 Solve: 2(w – 3) + 5 = 3(w – 1) 2w - 6 + 5 = 3w – 3 2w - 1 = 3w – 3 – 2w – 2w -1 = w – 3 + 3 + 3 2 = w

  14. Example 3 Solve: 8(5c – 2) = 10(32 + 4c) 40c – 16 = 320 + 40c – 40c – 40c -16 = 320 No solution

  15. Example 4 Solve: All Real Numbers

  16. Homework Pgs. 152-153: 16-42 Evens

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