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Solving Linear Inequalities and Graphing Solutions

Learn how to solve linear inequalities, perform transformations, and graph solutions. Understand compound inequalities and apply these skills to real-life scenarios.

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Solving Linear Inequalities and Graphing Solutions

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  1. Warm Up Solve. 1. A=lw for w 2. 3. 4. -3v + 6 = 4v – 1 5. 3(2x – 4) = 4x + 4

  2. Answers

  3. 1.5 Solving Linear Inequalities Textbook Page 33 August 26, 2015

  4. Inequality Symbols Less than Not equal to Less than or equal to Greater than or equal to Greater than

  5. Linear Inequality • Inequality with one variable to the first power. for example: 2x-3<8 • A solution is a value of the variable that makes the inequality true. x could equal -3, 0, 1, etc.

  6. Transformations for Inequalities • Add/subtract the same number on each side of an inequality • Multiply/divide by the same positive number on each side of an inequality • If you multiply or divide by a negative number, you MUSTflip the inequality sign!

  7. Lets look at things you can do with Inequalities 4 < 20 You can add the same number to both side of the inequality and not change the sign 4 + 8 < 20 + 8 12 < 28 You also subtract from both side with changing the sign 12 – 5 < 28 – 5 7 < 23

  8. Multiplication and Division are different When you multiply by a positive number the sign stays the same 4 < 20 4 * 2 < 20 * 2 8 < 40 But when you multiply or divide by a negative number, the sign changes direction 4 < 20 4 * - 2 < 20 * - 2 - 8 > - 40

  9. Ex: Solve the inequality. 2x-3<8 +3 +3 2x<11 2 2 x< Flip the sign after dividing by the -3!

  10. Graphing Linear Inequalities • Remember: < and > signs will have an open dot o and signs will have a closed dot graph of graph of 4 5 6 7 -3 -2 -1 0

  11. Textbook Page 35 #3A

  12. Textbook Page 36 #9 Tara is delivering bags of mulch. Each bag weighs 48 pounds and the push cart weighs about 65 pounds. If her flat bed truck is capable of hauling 2000 pounds, how many bags of mulch can Tara safely take on each trip?

  13. Example: Solve and graph the solution. 6 7 8 9

  14. Compound Inequality • An inequality joined by “and” or “or”. Examples “and” “or” think between think oars on a boat -3 -2 -1 0 1 2 3 4 5 -4 -3 -2 -1 0 1 2

  15. Example: Solve & graph. -9 < t+4 < 10 -13 < t < 6 Think between! -13 6

  16. Last example! Solve & graph. -6x+9 < 3 or -3x-8 > 13 -6x < -6 -3x > 21 x > 1 or x < -7 Flip signs Think oars -7 1

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