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Solving Equations with Steps

Learn to solve equations effectively using Barb's unique step-by-step approach. This guide covers the essential definitions of equations, inverses, and the hierarchy of operations (PEMDAS) while clearly illustrating the steps to isolate variables. Using examples like 4x + 5 = 15, you'll not only understand why it’s an equation but also how to solve it. Get tips on checking your work and practice problems to reinforce your skills. Empower yourself with the confidence to tackle math equations easily and accurately!

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Solving Equations with Steps

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  1. Solving Equations with Steps (Barb’s Nazi Way…) Have a white board/marker/wipe and a calculator…

  2. Definitions • An EQUATION is a math sentence. • It contains two expressions, separated by the equals sign (=). • The WALL is merely two parallel bars drawn to separate the two expressions. • INVERSES are operations that undo each other. • P--E--MD--AS is done backwards.

  3. Just Checking… • What is an equation? • How is it different from an expression? • What is the wall? • What are inverses? • Give 3 examples of inverses. • How is P--E--MD--AS done?

  4. Example: 3x + -2 = -7 • Why is this an equation? • What are the two expressions in this equation? • Which one of the expressions is in simplest form?

  5. Steps to solve equations: • Copy the problem. • Draw the wall. • Recopy the problem (leave a little space on the left). • Do backwards! Use inverse operations on both sides of the equal sign. • Solve like expressions - answer underneath. • Cloud answer. • Write the check and arrow up to original answer. P E MD AS

  6. Solve 4x + 5 = 15

  7. Solve 4x + 5 = 15

  8. Solve 4x + 5 = 15 4x + 5 - 5 = 15

  9. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5

  10. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10

  11. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10

  12. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4

  13. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4

  14. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4 1 1

  15. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4 1x = 2.5 1 1

  16. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4 1x = 2.5 x = 2.5 1 1

  17. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4 1x = 2.5 x = 2.5 1 1

  18. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4 1x = 2.5 x = 2.5 1 1 Check: 4 • 2.5 + 5 10 + 5 = 15

  19. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4 1x = 2.5 x = 2.5 1 1 Check: 4 • 2.5 + 5 10 + 5 = 15

  20. Solve 4x + 5 = 15 4x + 5 - 5 = 15 - 5 4x + 0 = 10 4x = 10 4 4 1x = 2.5 x = 2.5 It checks! 1 1 Check: 4 • 2.5 + 5 10 + 5 = 15

  21. Try these: • 125 + 3b = 154.97 • 4t + 7 = 3 • 15 = 3y - (-6) • n / (-8) + 2 = -3 • 30 = x / 3 - 9 • -4.2 = 23 + 8a Bonus: 3n + 9 + 4n = 2

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