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Algebra Chapter 6

Algebra Chapter 6. Warm Up. Solving Equations: 4(5-x) = 12 4x + 5x – 1= 53 6x – 2x + 8 = 36. Warm Up. Determine whether 5 is a solution to the inequality: 3x + 2 < 18 4x + 4 > 24 8 + x < 12. Re-teach. An open dot is used for < or >. A solid dot is used for ≥ or ≤

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Algebra Chapter 6

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  1. Algebra Chapter 6

  2. Warm Up Solving Equations: • 4(5-x) = 12 • 4x + 5x – 1= 53 • 6x – 2x + 8 = 36

  3. Warm Up Determine whether 5 is a solution to the inequality: • 3x + 2 < 18 • 4x + 4 > 24 • 8 + x < 12

  4. Re-teach An open dot is used for < or >. A solid dot is used for ≥ or ≤ Draw a picture representation of what each would look like on a graph.

  5. Re-teach Solving inequalities is similar to solving an equation. Example: 3x – 5 = 14 Example: 3x – 5 < 14

  6. Practice b-5 < -2 Solving Inequalities Step 1- Solve for the variable Step 2- Graph in the direction of the arrow or fill in 0 for the variable and graph

  7. Re-teach b-5 < -2 Step 1- Solve for the variable. b < 3 Step 2- Graph in the direction of the arrow or fill in 0 for the variable and graph. Ex: 0 < 3

  8. Practice • x + 6 <8 2. x – 5 ≥ 1 3. – 10 > a -6 **HINT** If the variable comes second re-arrange the problem.

  9. Warm Up Solving Multi-Step Equations • 7 – 3x = 16 • 2x + 10 = 7(x + 1) • 6x + 5 = 23

  10. Re-teach When multiplying or dividing by a negative, the symbol needs to flip sides. Example: 5 – x > 4

  11. Re-teach When multiplying or dividing by a negative, the symbol needs to flip sides. Example: -6 – 5x < 23

  12. Practice • 4x – 1 ≤ -17 • -x + 6 > -(2x + 4) • -x + 9 ≥ 14 • -5 ≤ 6x - 12

  13. Warm Up Write an inequality that represents the statement. x is less than 8 and greater than 3 x is less than 5 or less than 2 x is greater than -6 and less than -1

  14. Re-teach What is a compound inequality? What is the difference between “and” and “or” inequalities?

  15. Re-teach Example: -2 ≤ 3x – 8 ≤ 10 Solving Compound Inequalities Step 1- Determine if the inequality is an “and” versus “or” Step 2- Add or subtract the number on both sides Step 3- Multiply or divide on both sides to get the variable by itself Step 4- Graph the equation

  16. Re-teach -2 ≤ 3x – 8 ≤ 10 Step 1- Determine if the inequality is an “and” versus “or” The equation is “and”

  17. Re-teach -2 ≤ 3x – 8 ≤ 10 Step 2- Add or subtract the number on both sides 6 ≤ 3x ≤ 18

  18. Re-teach 6 ≤ 3x ≤ 18 Step 3- Multiply or divide on both sides to get the variable by itself 2 ≤ x ≤ 6

  19. Re-teach 2 ≤ x ≤ 6 Step 4- Graph the equation

  20. Practice • -5 < x – 3 < 6 2. – 4 < 2 + x < 1 3. – 4 ≤ -3x – 13 ≤ 26

  21. Re-teach Solving Compound Inequalities Step 1- Determine if the inequality is an “and” versus “or” Step 2- Add or subtract the number on both sides Step 3- Multiply or divide on both sides to get the variable by itself Step 4- Graph the equation

  22. Re-teach 3x + 1 <4 or 2x -5 > 7 Step 1- Determine if the inequality is an “and” versus “or” “or”

  23. Re-teach 3x + 1 <4 or 2x -5 > 7 Step 2- Add or subtract the number on both sides 3x + 1 < 4 2x – 5 > 7 3x < 3 2x > 12

  24. Re-teach Step 3- Multiply or divide on both sides to get the variable by itself 3x < 3 2x > 12 x < 1 x > 6

  25. Re-teach Step 4- Graph the equation

  26. Practice • -3< x + 6 or 2x > 4 • 2x – 6 < -8 or 10 – 5x < -19 • 6x – 2 > -7 or 3x – 1 > 11

  27. Re-teach When you multiply or divide by a negative the inequality symbol should be switched. Example: -2 < -2 – x < 1 Step 1- Determine if the inequality is an “and” versus “or” Step 2- Add or subtract the number on both sides Step 3- Multiply or divide on both sides to get the variable by itself Step 4- If you multiply or divide by a negative flip the inequality symbol. Step 5- Graph the equation

  28. Re-teach -2 < -2 – x < 1 Step 1- Determine if the inequality is an “and” versus “or” “and”

  29. Re-teach Step 2- Add or subtract the number on both sides -2 < -2 – x < 1 0 < - x < 3

  30. Re-teach Step 3- Multiply or divide on both sides to get the variable by itself. Step 4- If you multiply or divide by a negative flip the inequality symbol. 0 < - x < 3 0 > x > -3

  31. Re-teach Step 5- Graph the equation

  32. Practice • –15 ≤ –3x – 21 ≤ 25 • 6 < -x – 6 < 8 • -4 ≤ 2x ≤ 18

  33. Warm Up What is absolute value? Absolute Value l -28l l-74l l 15l

  34. Re-teach Solving Absolute Value Equations Step 1- Clear everything except for the absolute value on the one side of the equal sign. Step 2- Set the equation equal to a positive and a negative Step 3- Solve the equation for the variable Step 4- Write the two possible solutions

  35. Re-teach Example: Step 2- Set the equation equal to a positive and a negative

  36. Re-teach Step 3- Solve the equation for the variable x = 7 x = -3

  37. Re-teach Step 4- Write the two possible solutions x = 7 x = -3 The two possible solutions are 7 and -3

  38. Re-teach Example: Step 1- Clear everything except for the absolute value on the one side of the equal sign Step 2- Set the equation equal to a positive and a negative Step 3- Solve the equation for the variable Step 4- Write the two possible solutions

  39. Re-teach Step 1- Clear everything except for the absolute value on the one side of the equal sign.

  40. Re-teach Step 2- Set the equation equal to a positive and a negative

  41. Re-teach Step 3- Solve the equation for the variable 2x = -2 2x = 16 x = -1 x = 8

  42. Re-teach Step 4- Write the two possible solutions The two possible solutions are -1 and 8

  43. Practice

  44. Re-teach Absolute Value Inequalities Step 1- Clear everything except for the absolute value on the one side of the equal sign Step 2- Set the equation equal to a positive and a negative Step 3- Solve the equation for the variable Step 4- Reverse the inequality symbol on the negative Step 5- Write the compound inequality Step 6- Graph

  45. Re-teach Example: Step 1- Clear everything except for the absolute value on the one side of the equal sign

  46. Re-teach Step 2- Set the equation equal to a positive and a negative

  47. Re-teach Step 3- Solve the equation for the variable Step 4- Reverse the inequality symbol on the negative. x ≥ 4 x ≤ -5

  48. Re-teach Step 5- Write the compound inequality x ≥ 4 or x≤ -5 Step 6- Graph

  49. Practice

  50. Warm Up What is a linear inequality? What is a solution to a linear inequality?

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