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3.3 Using the Properties Together

3.3 Using the Properties Together. Goals: To solve equation by using the addition and multiplication properties To solve equation by collecting like terms To solve equations by distributing. Steps to Solve Multi-Step Equations. Distribute Collect like terms on each side of the =

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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 • To solve equations by distributing

  2. Steps to Solve Multi-Step Equations • Distribute • Collect like terms on each side of the = • Add/ Subtract (APE) • Multiply / Divide (MPE)

  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 Solve: -5x + 6 = 21 -5x + 6 = 21 - 6- 6 -5x = 15 x = -3

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

  7. 5 5 9x - 4x = 20 5x = 20

  8. +5 +5 9x + 3x – 5 = 19 12x – 5 = 19 12x = 24 x = 2

  9. 2(2y + 3) = 14 When there are parenthesis, you will normally apply the distributive property first. 4y + 6 = 14 4y = 8 y = 2

  10. +16 +16 Solve: 8(3x - 2) = 56

  11. 10 10 4(x - 2) + 3(2x + 1) = 5 • Distribute • Collect like terms on the same side of equation. • Add the opposite of any number being added to “x” • Divide both sides by the coefficient of “x”. 4x - 8 + 6x + 3 = 5 10x – 5 = 5 10x – 5 +5 = 5 + 5 10x = 10 x = 1

  12. +23 +23 1 1 3(2x - 1) - 5(x + 4) = 61 6x - 3 - 5x - 20 = 61 • Distribute • Collect like terms on the same side of equation. • Add the opposite of any number being added to “x” • Divide both sides by the coefficient of “x”. 1x -23 = 61 1x = 84 x = 84

  13. Assignment:Page 127#’s (4-40) even

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