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Mastering Linear Equations with Distributive Property

Learn how to solve linear equations using the distributive property, combining like terms, and inverse operations. Practice simplifying expressions and solving equations step by step with examples and interactive activities.

robertwatkins
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Mastering Linear Equations with Distributive Property

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  1. Solving equations • 8.M.EE.07 “I can solve linear equations using the distributive property and by combining like terms.”

  2. The basics 3x + 2x = 12 • The Vocabulary: • Variable - the “placeholder” for what we are trying to solve. • Coefficient - the number before the variable. Written next to it, it means its being multiplied. • Like Terms - terms in an equation that have similar qualities. • Inverse Operations - addition/subtraction and multiplication/division

  3. Solving an equation • Use Distributive Property and PEMDAS to simplify each side of the equation. • Combine like terms • Use inverse operations to isolate the variable on one side of the equation. • Here’s an example: • 2(3x - 3) = -12

  4. DISTRIBUTIVE PROPERTY Example: 7(3x - 4) = 21x - 28

  5. PRACTICE • On your whiteboard, simplify the following expressions using the distributive property. • 9(x -1) • 7(2x - 7) • 9(6 - x)

  6. like terms • terms with the same variables and exponents x 3x 9 7x 14 5 Which of these are like terms?

  7. like terms • Simplify the following expressions by combining like terms. • 3x - 4 + 7x + 2 • 9x - 1 + x • x + 2x - 4 + 9

  8. Example 2 : 3 + x = 5 2 inverse operations • Add/Subtract • Multiply/Divide Example 1 : 7x - 14 = 21

  9. Putting it all together • Solve the following equations: • 3x - 4 = 5 • 2(2x + 6) = 16 • 7(x + 1) - 4 = 24

  10. What about this? • What if there is a variable on both sides of the equation? • 17x - 8 = 14x + 1

  11. Practice • 7x - 4 = x + 2 • 9 - x = 2x + 3 • 2x + 3(x + 2) = 11

  12. CLOSURE • Partner Pass - with your seat partner solve the problem below. Each of you completes one step and passes the whiteboard to the other. • 2(x + 4) = 14 + x

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