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Algebra 5 Points 1 And 2
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Algebra 5 Points 1 And 2

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  • 1. 5.1 Addition and Subtraction Problems of Inequality
    Objective:
    • To solve and graph the solution set of an inequality by using the Addition or Subtraction Property of Inequality
    Frameworks: 10.P.1, 10.P.7
  • 2. How do you read . . .
    a < b
    a is less than b
    a > b
    a is greater than b
  • 3. Inequality
    The open sentence
    x < -2
    is an example of an inequality
    An inequality contains at least one variable and consists of 2 expressions with an inequality symbol such as <, >, or ≠ between them.
  • 4. Solving an Inequality
    To solve an inequality means to find a solution set.
    What is the solution set of x < -2?
    On a number line:
    open circle means
    not including this point
  • 5. Solving an Inequality
    How would we graph the solution of x > 1?
  • 6. Solving an Inequality
    The Addition and Subtraction Properties of Equality allow you to add or subtract the same number from each side of an equation to obtain an equivalent equation.
    x – 4 = 3 x + 2 = 5
    Do inequalities work the same way?
  • 7. Solving an Inequality
    2 < 6
    +5 +5
    7 < 11
    TRUE
  • 8. Solving an Inequality
    2 < 6
    -1 -1
    1 < 5
    TRUE
  • 9. Equivalent Inequalities
    Open inequalities with the same solution set are called equivalent inequalities.
  • 10. Addition Property of Inequality
    For all real numbers a, b, and c,
    if a < b, then a + c < b + c, and
    if a > b, then a + c > b + c
    In other words, adding the same number to each side of an equality produces an equivalent equality.
  • 11. Subtraction Property of Inequality
    For all real numbers a, b, and c,
    if a < b, then a - c < b - c, and
    if a > b, then a - c > b - c
    In other words, subtracting the same number from each side of an equality produces an equivalent equality.
  • 12. Solve x – 8 > -11 & Graph
  • 13. Solve & Graph 7 < 5 – (½ – x)
  • 14. After Mary paid $8.36 for a snack she had less than $2.50 left. How much money did she have originally?
  • 15. After Bill paid $7.21 at the movies, he had less than $1.75 left. How much money did he have originally?
  • 16. 5.2 Multiplication & Division Problems of Inequality
    Objective:
    • To solve and graph the solution set of an inequality by using the Multiplication or Division Property of Inequality
    Frameworks: 10.P.1, 10.P.7
  • 17. Solving an Inequality
    The Multiplication and Division Properties of Equality allow you to add or subtract the same number from each side of an equation to obtain an equivalent equation.
    x / 4 = 2 x * 3 = 21
    Do inequalities work the same way?
  • 18. Solving an Inequality
    3 < 4
    *5 *5
    15 < 20
    TRUE
  • 19. Solving an Inequality
    -4 > -20
    /2 /2
    -2 > -10
    TRUE
  • 20. Solving an Inequality
    -5 < -3
    *-1 *-1
    5 < 3
    FALSE
  • 21. Solving an Inequality
    18 > -6
    /-3 /-3
    -6 > 2
    FALSE
  • 22. Notice:
    Multiplying or Dividing each side of a true equality by a negative number produces a false inequality
  • 23. Multiplication Property of Inequality, Part 1
    For all real numbers a, b, and c,
    if a < b and c > 0, then ac < bc, and
    if a > b and c > 0, then ac > bc
    That is, multiplying each side of an inequality by the same positive number produces an equivalent inequality.
  • 24. Multiplication Property of Inequality, Part 2
    For all real numbers a, b, and c,
    if a < b and c < 0, then ac > bc, and
    if a > b and c < 0, then ac < bc
    That is, multiplying each side of an inequality by the same negative number and reversing the order of the inequality produces an equivalent inequality.
  • 25. Division Property of Inequality, Part 1
    For all real numbers a, b, and c,
    if a < b and c > 0, then a/c < b/c, and
    if a > b and c > 0, then a/c > b/c
    That is, dividing each side of an inequality by the same positive number produces an equivalent inequality.
  • 26. Division Property of Inequality, Part 2
    For all real numbers a, b, and c,
    if a < b and c < 0, then ac > b/c, and
    if a > b and c < 0, then ac < b/c
    That is, dividing each side of an inequality by the same negative number and reversing the order of the inequality produces an equivalent inequality.
  • 27. Solve:
    7x < -56
    Divide each side by 7
    x < -8
    Graph:
  • 28. Solve:
    -⅔ x > 16
    Multiply each side by the reciprocal of -⅔
    Because we multiplied by a negative, change the > to a <
    x < -24
    Graph:
  • 29. Solve:
    -4 < - 2x
  • 30. If Jill sells more than $100 worth of peanut brittle, she will win a radio. Each box of peanut brittle sells for $2.75. How many boxes must she sell to win the radio?
    2.75p > 100
    p > 100/2.75
    p > 36.3636
    Can she sell 36.36 boxes?
    Jill must sell 37 boxes.
  • 31. -3x + 6 < -5
  • 32. 5 – 4x < 2x - 7
  • 33. -3/2 x + 4 > 7
  • 34. -2(2x + 1) + 5x < x + 5
  • 35. Turn to p. 168
    Do 1 -14
    Turn to p. 169
    Do 16-19
    Turn to p. 173
    Do 1-9
    Turn to p. 174
    Do 27-30