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Comprehensive Guide to Solving Equations: Step-by-Step Assistance

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Discover the fundamental techniques for solving equations, including step equations and the distributive property. Learn how to isolate variables by undoing operations in reverse order. This guide covers examples of 1-step and 2-step equations, providing practice problems for hands-on experience. You'll find tips on combining like terms and resources such as Kahn Academy videos for visual learning. Master these skills to enhance your mathematical proficiency and confidently tackle equations with various complexities.

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Comprehensive Guide to Solving Equations: Step-by-Step Assistance

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Presentation Transcript

  1. Solving Equations Unit 10

  2. Objective to Solving Equations You must undo all operations in the problem to isolate the variable. You ultimately do order of operations backwards.

  3. 1 Step Equations Add Subtract X – 8 = 25M + 15 = 39 + 8 + 8 -15 -15 X = 33 M = 24 Multiply Divide G / 3= 12 3G = 54 *3 *3 ÷ 3 ÷ 3 G = 36 G = 18

  4. Kahn Academy Video Solving Equations

  5. 2 Step Equation2 Operations to undo Ex. 1 Ex. 2 Ex 2. 5r – 10 = 30 + 10 = + 10 5r = 40 ÷5 ÷5 r = 8 Ex 1. 3w + 15 = 39 -15 -15 3w = 24 ÷ 3 ÷ 3 w = 8

  6. 2 Step equations Video 2 step equations

  7. Practice Problems – on a piece of paper, answer the following. Show your work! • -25 = 7x 18 • 3K + 42 = 54 • 78 – 12m = 102 • ½ R + 19 = - 3 • -5B – 44 = 16 • 45 = -8L + 9

  8. Check your answers. • X = -1 • K = 4 • m = -2 • R = -44 • B = -12 • L = -4.5

  9. Distributive Property 2 (3x + 4) …..everything inside gets multiplied by what’s on the outside Ex. 2 3(5x – 8) = 3* 5x – 3* 8 = 15x – 24 2 (3x + 4) = 2 * 3x + 2 * 4 = 6x + 8

  10. Distributive Property Video

  11. Distributive property/solving equations Ex 1. 2(4x – 4) = 24 (distribute first) ( 2 steps) Ex 2. 4(3x + 5) = 68 Ex. 3 -3(2x + 9) = 9

  12. Kahn Academy Video • Insert Video

  13. Practice Problems Insert practice problems

  14. Check Answers • Answer to practice problems

  15. Combining like terms Like terms have the same variable and same exponent 2x and 4x – YES, 6x 4m and 5m – YES, 9m 7g and -10g – YES, -3g 4x and 5x2 – NOT LIKE TERMS BECAUSE OF EXPONENTS

  16. Combine like terms in equations Ex. 1 4x + 8 + 3x = 22 Ex. 2 3m + 6m + 2 = 20 Ex.3 10 + 10g – 5g = 50

  17. Distribute and like terms Ex. 1 4(2x + 5) – 10 = 26 Ex. 2 5(x – 5) + 3x = 15 Ex. 3 6(2x – 5) – 10x = 2

  18. Kahn Academy Video • Insert video

  19. Practice Problems Insert Practice Problems

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