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3.3 Using the Properties Together

This guide focuses on solving equations through the addition and multiplication properties and collecting like terms. Key steps involve identifying like terms, applying addition (APE) and multiplication (MPE) to both sides of the equation, and following a structured process for solving two-step equations. Examples include solving equations like 3x + 4 = 13 by isolating the variable, and practicing with various problems on Page 127. Master these techniques to improve your algebra skills effectively.

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3.3 Using the Properties Together

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  1. 3.3 Using the Properties Together Goals: • To solve equation by using the addition and multiplication properties • To solve equation by collecting like terms

  2. Steps to Solving Tonight’s Equations • If you see like terms on the same side of the equation collect them • Add or Sub using APE to both sides • Multiply or Divide using MPE to both sides

  3. 3x + 4 = 13 2-step equations: Always do the add/subtract step before multiplying by the inverse of the coefficient.

  4. 3 3 Solve: 3x + 4 = 13 3x + 4 = 13 - 4- 4 3x = 9 x = 3

  5. 5 5 5x + 11 = 31 5x + 11 = 31 - 11- 11 5x = 20 x = 4

  6. -5 -5 -5x + 6 = 21 -5x + 6 = 21 - 6- 6 -5x = 15 x = -3

  7. If there are like terms on one side of the equation, collect them before using the properties 6x + 2x = 16 8x = 16 x = 2

  8. 5 5 9x - 4x = 20 5x = 20

  9. 9x + 3x – 5 = 19 +5 +5 12x – 5 = 19 12x = 24 x = 2

  10. Assignment:Page 127#’s 2-24 even in the four columns

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