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Solving equations

Solving equations. 8.M.EE.07 “I can solve linear equations using the distributive property and by combining like terms.”. The basics. 3x + 2x = 12. The Vocabulary: Variable - the “placeholder” for what we are trying to solve.

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Solving equations

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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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