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Solving Linear Equations

Solving Linear Equations. You already know how, but do you know why????. 3x + 4 = 31. Solve this equation!. Steps we took to solve the equation: Subtract 4 from both sides of the equation Divide by 3 on both sides of the equation. Why did you do what you did?.

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Solving Linear Equations

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  1. Solving Linear Equations You already know how, but do you know why????

  2. 3x + 4 = 31 Solve this equation!

  3. Steps we took to solve the equation: • Subtract 4 from both sides of the equation • Divide by 3 on both sides of the equation Why did you do what you did?

  4. Subtraction Property of Equality • If a=b, then a-c=b-c • Division Property of Equality • If a=b and c0, then a÷c=b÷c Properties of Equality

  5. Reflexive Property of Equality • a=a • Symmetric Property of Equality • If a=b, then b=a • Transitive Property of Equality • If a=b and b=c, then a=c • Addition Property of Equality • If a=b, then a+c=b+c • Multiplication Property of Equality • If a=b, then ac=bc • Substitution Property of Equality • If a=b, then b may be substituted for a in any expression containing a. Other Properties of Equality

  6. They allow us to provide justifications for our steps of solving equations in an organized and methodical manner. • To justify our answer means to prove why what we did is correct and works. Two Column Proofs

  7. Two Column Proofs

  8. Solve and Justify Using a Two Column Proof: • 8x – 1 = 23 – 4x Now you try!

  9. Think-Ink-Pair-Share • With each of the next problems, think about how to solve it and the justifications that are needed. Create a two column proof for the problem. • You will then pair up with your partner to check each other on the work you did. • We will then get one person or pair to come up and show how they worked the problem to make sure everyone in the class gets it. Practice!!

  10. 5u + 3 = 48 • 3f = 4 + f • - 2 = 6 • 12b + 21 = -2b – 21 • 5x – 20 = + 8 Practice Problems

  11. An equation that has no numbers and only has variables. • Examples: • C=2r • A=r2 • V=lwh Literal Equations

  12. V=lwh • What inverse operations are needed to do this? Solve the literal equation above for “l”

  13. A = r2 • What inverse operations are needed to do this? Solve the literal equation above for “r”

  14. Ms. Rogers and Ms. Bradbury bought 25 total pencils to share with their classes. If Ms. Rogers bought 17, how many did Ms. Bradbury purchase? Real World Applications

  15. Ms. Herrington bought 6 shirts for an unknown amount of money each. She also bought a pair of pants that cost her 30 dollars. If her entire purchase cost $60, how much did each of her shirts cost? (Don’t worry about tax here, because she was a smart shopper and went on tax free weekend!) Real World Applications

  16. Copy these problems down to do for homework. • You will need to solve each equation for the variable and create a two column proof to show the justifications to your steps. • 6r + 4 = -r – 24 • + 8 = 2 • a + 5 = -5a + 5 • PV=nrt (Rearrange for t) • 5p – 14 = 8p + 4 Homework

  17. Match the steps of solving an equation to the justifications for that step. • Then answer the question below. Summarizer

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