5.1 Addition and Subtraction Problems of Inequality<br />Objective:  <br /><ul><li>To solve and graph the solution set of ...
       How do you read . . .<br />a < b<br />    a is less than b<br />a > b<br />     a is greater than b<br />
Inequality<br />The open sentence <br />         x < -2<br />               is an example of an inequality<br />An inequal...
Solving an Inequality<br />To solve an inequality means to find a solution set.<br />What is the solution set of x < -2?<b...
Solving an Inequality<br />How would we graph the solution of x > 1?<br />
Solving an Inequality<br />The Addition and Subtraction Properties of Equality allow you to add or subtract the same numbe...
Solving an Inequality<br />   2  <  6         <br />  +5    +5<br />   7  <  11<br />    TRUE<br />
Solving an Inequality<br />   2  <  6         <br />  -1      -1<br />   1  <  5<br />    TRUE<br />
Equivalent Inequalities<br />Open inequalities with the same solution set are called equivalent inequalities.<br />
Addition Property of Inequality<br />For all real numbers a, b, and c,<br />    if a < b, then a + c < b + c, and<br />   ...
Subtraction Property of Inequality<br />For all real numbers a, b, and c,<br />    if a < b, then a - c < b - c, and<br />...
Solve x – 8 > -11 & Graph<br />
Solve & Graph 7 < 5 – (½ – x)    <br />
After Mary paid $8.36 for a snack she had less than $2.50 left.  How much money did she have originally?<br />
After Bill paid $7.21 at the movies, he had less than $1.75 left.  How much money did he have originally?<br />
5.2 Multiplication & Division Problems of Inequality<br />Objective:  <br /><ul><li>To solve and graph the solution set of...
Solving an Inequality<br />The Multiplication and Division Properties of Equality allow you to add or subtract the same nu...
Solving an Inequality<br />   3 < 4<br />  *5    *5<br />  15 < 20<br />    TRUE<br />
Solving an Inequality<br />   -4 > -20<br />    /2    /2<br />  -2 > -10<br />    TRUE<br />
Solving an Inequality<br />   -5 < -3<br />    *-1   *-1<br />    5  <  3<br />FALSE<br />
Solving an Inequality<br />   18 > -6<br />    /-3   /-3<br />    -6  >  2<br />FALSE<br />
Notice:<br />Multiplying or Dividing each side of a true equality by a negative number produces a false inequality<br />
Multiplication Property of Inequality, Part 1<br />For all real numbers a, b, and c,<br />if a < b and c > 0, then ac < bc...
Multiplication Property of Inequality, Part 2<br />For all real numbers a, b, and c,<br />if a < b and c < 0, then ac > bc...
Division Property of Inequality, Part 1<br />For all real numbers a, b, and c,<br />if a < b and c > 0, then a/c < b/c, an...
Division Property of Inequality, Part 2<br />For all real numbers a, b, and c,<br />if a < b and c < 0, then ac > b/c, and...
Solve:<br />7x < -56<br />Divide each side by 7<br />x < -8<br />Graph:<br />
Solve:<br />-⅔ x > 16<br />Multiply each side by the reciprocal of -⅔ <br />Because we multiplied by a negative, change th...
Solve:<br />-4 < - 2x<br />
If Jill sells more than $100 worth of peanut brittle, she will win a radio.  Each box of peanut brittle sells for $2.75.  ...
-3x + 6 < -5<br />
5 – 4x < 2x - 7<br />
-3/2 x + 4 > 7<br />
-2(2x + 1) + 5x < x + 5<br />
Turn to p. 168<br />Do 1 -14<br />Turn to p. 169<br />Do 16-19<br />Turn to p. 173<br />Do 1-9<br />Turn to p. 174<br />Do...
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Algebra 5 Points 1 And 2

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Algebra 5 Points 1 And 2

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