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Lesson 1: One Step Equations (+ & -)

Solving Multi-Step Equations. Lesson 1: One Step Equations (+ & -). Lesson 1: Properties of Equality. Addition Property of Equality If a = b, then a + c = b + c Example: If 2=2, then 2+1=2+1 This is true: 3=3

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Lesson 1: One Step Equations (+ & -)

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  1. Solving Multi-Step Equations Lesson 1: One Step Equations(+ & -)

  2. Lesson 1: Properties of Equality Addition Property of Equality • If a = b, then a + c = b + c • Example: If 2=2, then 2+1=2+1 • This is true: 3=3 *If any number is added to both sides of an equal sign, then both sides will remain equal Subtraction Property of Equality • If a = b, then a - c = b - c • Example: If 2=2, then 2-1=2-1 • This is true: 1=1 *If any number is subtracted from both sides of an equal sign, then both sides will remain equal Continue with lesson 1

  3. Lesson 1: Using Addition Property of Equality in 1 Step Equation Example 1 Solve for X: X – 2 = 10 +2+2 X – 2 + 2 = 10 +2 X = 12 Rationale • We are solving for X so we need to get X by itself • We need to add 2 to the left side of the equal sign so that the -2 and +2 will become zero and X will be alone • In order for the equation to remain equal, we must also add 2 to the right side of the equal sign Continue with lesson 1

  4. Using Subtraction Property of Equality in 1 Step Equation Example 1 Solve for X: X + 5 = 10 -5-5 X + 5 – 5 = 10 -5 X = 5 Rationale • We are solving for X so we need to get X by itself • We need to subtract 5 to the left side of the equal sign so that the +5 and -5 will become zero and X will be alone • In order for the equation to remain equal, we must also subtract 5 from the right side of the equal sign Extra Practice + Take Quiz 1 Restart Lesson 1 Extra Practice -

  5. Quiz 1 1. Solve for X: X+7 = 10 X = 17 X = 3 X = -7

  6. Try again. You can do it. Just remember: You must perform the opposite operation to both sides of the equal sign* YouTube on subtraction property of equality Return to Lesson 1

  7. You are correct! When solving X+7 = 10, you must subtract 7 from each side in order to get X by itself and the answer becomes 3 (10-7). Proceed to Question 2

  8. Quiz 1 2. Solve for X: X-15 = 27.5 X = 42.5 X = 12.5 X = 13.5

  9. You are incorrect!! Try again. You can do it! YouTube on addition property of equality Lesson 1 Refresher

  10. Lesson 1 Refresher! Step 1:X – 3 = 4 Step 2: Add 3 to the left to cancel out the -3. Add 3 to right to keep the equation equal (balanced) - - + + + + - X + + + + + + X - + + - + + - Step 3: Since the +3 and -3 cancel out on the left, you only have X. On the right add up the positives and you get…X=7 Back to question 2

  11. That’s Nice!! Continue to Lesson 2

  12. Lesson 2: Properties of Equality Division Property of Equality • If a = b, then a/c = b/c • Example: If 10=10, then 10/5=10/5 • This is true: 2=2 *If both sides of an equal sign are divided by the same number, then both sides will remain equal Continue with Lesson 2 Multiplication Property of Equality If a = b, then a ∙ c = b ∙ c Example: If 2=2, then 2 ∙ 4=2 ∙ 4 This is true: 8=8 *If any number is multiplied by both sides of an equal sign, then both sides will remain equal

  13. Lesson 2: Using Multiplication Property of Equality in 1 Step Equation Rationale • We need to get X by itself, however X is divided by 2 • We need to multiply the left side of the equal sign by 2 so that it can cancel out the 2 in the denominator • In order for the equation to remain equal, we must also multiply the right side of the equal sign by 2 Continue with Lesson 2 Example 1 Solve for X: = 16 ∙ = ∙ 16 X = 32

  14. Lesson 2: Using Division Property of Equality in 1 Step Equation Rationale • We are solving for X so we need to get X by itself; however X is multiplied by 3 • We need to divide the left side of the equal sign by 3 so that it can cancel out the other 3, leaving us with only X • In order for the equation to remain equal, we must also divide the right side of the equal sign by 3, which equals 8 Extra Practice X Extra Practice ÷ Take quiz 2 Restart Lesson 2 Example 1 Solve for X: 3x= 24 = X = 8

  15. Quiz 2 1. Solve for X: 4X = 28 (Click on who answered correctly) X= 112 X = 4 X= 7

  16. Incorrect *Try again. You can do it. Just remember: You must perform the opposite operation to both sides of the equal sign* YouTube on division property of equality Return to Lesson 2

  17. Good Job! When solving 4X = 28, you must divide by 4 on each side. Proceed to question 2

  18. Quiz 2 2. Solve for X: = 4 12 18

  19. Try again. You can do it. Wrong YouTube on multiplication property of equality Lesson 2 Refresher

  20. Lesson 2 Refresher If the variable is multiplied by a number:4x=20 Add the number to both sides: +19 Divide both sides by the number ÷ 4 If a number is subtracted from the variable:X - 19 = 20 To solve one step equations, undo what is being done to the variable If the variable is divided by a number:X = 459 If a number is added to the variable:X + 5 = 10 Subtract the number from both sides: -5 Multiply both sides by the number:∙9 Back to question 2

  21. You’re Right Move on to lesson 3

  22. Lesson 3: What is a Reciprocal? Proceed with lesson 3

  23. Lesson 3: 1 step equations with reciprocals Example 1 X = 10 ∙ X = ∙ 10 X = X = 6 Example 2 X = 3 ∙ X = ∙ 3 X = X = -6 Restart lesson 3 Take lesson 3 quiz

  24. Quiz 3 1. Which of the following is false? • A number multiplied by its reciprocal yields the answer, 1 • In a one step equation, when a number is multiplied by its reciprocal, both number can be canceled out since they multiply to the answer, 1 • To find a reciprocal, you simply flip a fraction and change positive to negative or the negative to positive A B C

  25. Return to lesson 3 Be sure you watch the videos and carefully and reexamine the examples YouTube explanation of reciprocals

  26. You are right. When you find a reciprocal, you do NOT change the sign. Proceed to question 2

  27. Quiz 3 2. If a fraction is multiplied by a variable in a one step equation how do you solve the equation? A) Multiply each side by the reciprocal (of the fraction that is being multiplied by the variable) B) Multiply only the side with the variable by the reciprocal C) Multiply both sides by the reciprocal (of the number on the opposite side of the equal sign from the variable) A B C

  28. Well Done! Advance to lesson 4

  29. Try again. You can do it. Restart lesson 3 Lesson 3 Refresher

  30. Retake question 2

  31. Lesson 4: The Order of Operations in Two Step Equations PParenthesis EExponents MDMultiplicationDivisionLeft to Right ASAdditionSubtractionLeft to Right Proceed with lesson 4

  32. Lesson 4: Solving a 2 Step Equation 2X + 5 = 15 2X +5 – 5 = 15 – 5 2X = 10 22 X = 5 • We begin with addition/subtraction. To eliminate the +5, we must -5 from both sides • We proceed to multiplication/division. To cancel out the 2, we must divide each side by 2. Proceed with lesson 4

  33. Lesson 4: Solving a 2 Step Equation • We begin with addition/subtraction. To eliminate the -6, we must +6 to both sides • We proceed to multiplication/division. To cancel out the 3, we must multiply each side by 3. Extra Practice 1 Extra Practice 2 Take Quiz 4 - 6 = 12 -6 + 6 = 12 + 6 (3) = 18 (3) X = 54

  34. Quiz 4 • When solving for X in the two step equation, 4X + 12 = 16, what is the order of the two steps that must be performed? A: Add 12, then multiply by 4 B: Divide by 4, then subtract 12 C: Subtract 12, then divide by 4 A B C

  35. Proceed to Question 2

  36. Try again. You can do it! YouTube on solving two step equations Return to Lesson 4

  37. Quiz 4 2. Solve the equation, 5X-25 = 75 X = 10 X = 20 X = 5

  38. Well Done Continue to lesson 5

  39. You are incorrect. Review and try again. You can do it! Lesson 4 refresher Restart Lesson 4

  40. Lesson 4 Refresher *Remember to work backwards through the order of operations* PEMDAS 6X + 9 = 27 PEMDAS-9 from both sides 6X = 18 PEMDAS÷ 6 from both sides X = 9 Retake question 2 Restart lesson 4

  41. Lesson 5: Like Terms • Terms are single parts of an expression and are separated by +, -, ÷, and ∙ • There are 6 terms in the following expression… 3X + 5Y – X + 7 + Y – 1 • Like Terms: Terms whose variables are the same • Numbers are like terms since they have no variable • There are 3 pairs of like terms in the following expression… 3X+ 5Y–X+7+Y–1 Proceed with Lesson 5

  42. Lesson 5: Combining Like Terms • In an expression or equation, like terms can be combined… • Given 3X – 5 + 2X + 9 • Identify the like terms 3X– 5+2X+ 9 • Combine the like terms (3X & 2X) 5x– 5 + 9 • Combine like terms (-5 & 9)5x + 4 Proceed with Lesson 5

  43. Lesson 5: Like terms in multi-step equations *Combine like terms before working backwards through the order of operations* PParenthesis EExponents MDMultiply/DivideLeft to Right ASAdd/SubtractLeft to Right CLTCombine Like Terms Proceed with Lesson 5

  44. Lesson 5: Combining Like Terms Proceed to quiz 5

  45. Quiz 5 3X + 15 – 4X = 20 1. After combining the like terms from the following equation you will have… -X + 15 = 20 X + 15 = 20 -X + 35

  46. Congratulations!! Proceed to question 2

  47. INCORRECT Review the lesson and try again. You can do it. YouTube explains combining like terms Restart Lesson 5

  48. Quiz 5 2. Who is correct about the answer to the following equation 6X + 10 – X + 5 = 50? X = 7 X = 5 X = 13

  49. Well Done!! Proceed to Lesson 6

  50. Incorrect You can do it! Review and try again Lesson 5 Refresher Restart Lesson 5

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