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- 1. Solving One-Step Inequalities Section 2.9 and 2.10b <ul><li>Goal </li></ul><ul><li>Solve and graph one-step inequalities in one variable using addition or subtraction. </li></ul><ul><li>Key Words </li></ul><ul><ul><li>graph of an inequality </li></ul></ul><ul><ul><li>equivalent inequalities </li></ul></ul>
- 2. Graph an Inequality in One Variable Write a verbal phrase to describe the inequality. Then graph the inequality. 1. x < 2 INEQUALITY VERBAL PHRASE GRAPH 3. x 1 All real numbers greater than -2 -3 -2 -1 0 1 2 3 2. 4. EXAMPLE 1
- 3. Write a verbal phrase to describe the inequality. Then graph the inequality. <ul><li>t > 1 </li></ul><ul><li>x -1 </li></ul><ul><li>y 4 </li></ul><ul><li>n < 0 </li></ul>Checkpoint Graph an Inequality in One Variable.
- 4. A solution of an inequality in one variable is a value of the variable that makes the inequality true. Equivalent inequalities have the same solutions. EXAMPLE: x 5 and 5 x are equivalent inequalities.
- 5. PROPERTIES OF INEQUALITY Addition Property of Inequality For all real numbers a , b, and c : If a > b , then a + c > b + c If a < b , then a + c < b + c Subtraction Property of Inequality For all real numbers a , b, and c : If a > b , then a - c > b - c If a < b , then a - c < b - c
- 6. Use Subtraction to Solve an Inequality Solve x + 5 3. Then graph the solution. EXAMPLE 2
- 7. Solve the inequality. Then graph the solution. <ul><li>x + 4 < 7 </li></ul><ul><li>5 > a + 5 </li></ul><ul><li>n + 6 2 </li></ul>Checkpoint Use Subtraction to Solve an Inequality
- 8. Use Addition to Solve an Inequality Solve -2 > n – 4. Then graph the solution. EXAMPLE 3
- 9. Solve the inequality. Then graph the solution. <ul><li>x - 5 2 </li></ul><ul><li>-3 < y – 2 </li></ul><ul><li>p – 1 -4 </li></ul>Checkpoint Use Addition to Solve an Inequality
- 10. Write an Inequality with One Variable. Real-World Connection: Page 105: Nearly 32 megabytes (MB) of memory are available for running your computer. If its basic system requires 12.1 MB, how much memory is available for other programs? Memory for basic system PLUS Memory for other programs IS LESS THAN Total memory We don’t know m = memory available for other programs. 21.1 + m < 32 12.1 + m < 32 -12.1 -12.1 m < 19.9 There is LESS THAN 19.9 MB of memory available for other programs. EXAMPLE 4
- 11. <ul><li>Ms. Dewey-Hoffman is flying to San Diego to see her parents. Southwest lets me check up to 65 pounds of luggage. My suitcase with your homework that I have to grade weighs 37 pounds. How much can my other suitcase, with my clothes and toothbrush, weigh? </li></ul>1 st Suitcase: 37 Pounds PLUS 2 nd Suitcase: Unknown Weight IS LESS THAN Total weight of suitcases We don’t know the weight of the second suitcase, w. 37 + w < 65 -37 -37 w < 28 lb The 2 nd suitcase has to be no more than 28 pounds. Checkpoint Write and Graph an Inequality in One Variable
- 12. Multiply by a Positive Number EXAMPLE 1 Solve . Then graph the solution.
- 13. Divide by a Positive Number Solve: 4 x > 20 Then graph the solution. EXAMPLE 2
- 14. Solve the inequality. Then graph the solution <ul><li>18 2 k </li></ul><ul><li>-21 3 y </li></ul>Checkpoint Multiply or Divide by a Positive Number. <ul><li>6 < </li></ul>
- 15. PROPERTIES OF INEQUALITY Multiplication Property of Inequality ( c < 0) For all real numbers a , b, and for c < 0: If a > b , then ac < bc If a < b , then ac > bc Division Property of Inequality ( c < 0) For all real numbers a , b, and c < 0: If a > b , then a ÷ c < b ÷ c If a < b , then a ÷ c > b ÷ c
- 16. Things to remember about Multiplying and Dividing Inequalities! <ul><li>Dividing both sides of an inequality by a POSITIVE number and the inequality stays the same. </li></ul><ul><li>Dividing both sides of an inequality by a NEGATIVE number and the inequality flips and faces the other way. </li></ul><ul><li>Multiply both sides of an inequality by a POSITIVE number and the inequality stays the same. </li></ul><ul><li>Multiply both sides of an inequality by a NEGATIVE number and the inequality flips and faces the other way. </li></ul>
- 17. Example of Inequalities Flipping 36 -9t -9 ÷ 36 -9t ÷ -9 -4 t If you get confused by flipping the inequality, instead, you can just flip the sides the numbers are on and keep the inequality the same. t/ -3 < 7 (-3)t/ -3 < 7(-3) t > -21
- 18. Multiply by a Negative Number EXAMPLE 3 Solve . Then graph the solution.
- 19. Divide by a Negative Number EXAMPLE 4 Solve . Then graph the solution.
- 20. Solve the inequality. Then graph the solution Checkpoint Multiply or Divide by a Negative Number.
- 21. Solve the inequality. Then graph the solution <ul><li>12 > -5 n </li></ul>Checkpoint Multiply or Divide by a Negative Number.
- 22. Assignment #13: Pages 106-107: 9-21 odd (just solve, don’t graph), 28, 31. Pages 111-112: 13-27 all.

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