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Solving Inequalities of one variable (x)
- 1.
- 2. Inequality Signs An inequalityis like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to
- 3. “x < 5” meansthat whatever value x has, it must be less than 5. What could x be?
- 4. “x ≥ -2” meansthat whatever value x has, it must be greater than or equal to -2. What could x be?
- 5. Graphing Rules Symbol CircleDirection of Arrow < Open Left > Open Right ≤ Closed Left ≥ Closed Right
- 6. Examples: x <5 x > -2 x ≤ -8 x ≥ 4
- 7. You Try: x< -6 x > 2 x ≤ 0 x ≥ -7
- 8. Practice x +5 > 13 2x – 14 > 4 5 + x < 7 x /4 + 3 < 7
- 9. Use the KeyWords to Write an Inequality A number added to 5 is greater than 12 The quotient of 2 and a number is at most 6 7 multiplied by a number is less than 16 18 decreased by a number is no less than 12.8 17 is greater than or equal to 8 less than a number
- 10. Solving Inequalities! Solvinginequalities is the same as solving equations. There are only 2 things you need to know… 1.) If you multiply or divide by a negative number you must switch the sign. -7x < 21 -7 -7 x > -3 2.) You will graph your solutions. Dividing by a negative means switch the sign!!
- 11. Special Case 1:Switching the Signs When solving inequalities, if you multiply or divide by a negative you must switch the signs. Switching the signs: Less than becomes Greater than < switches to > Greater than becomes Less than > switches to < Less than or equal to becomes Greater than or equal to ≤ switches to ≥ Greater than or equal to becomes Less than or equal to ≥ switches to ≤
- 12. Division Property forInequalities Caution! Dividing by a negative number 20 5 x 5 20 5 5 x 4 x Notice: Symbol CHANGED Same if multiplying?
- 13. Multiplication Property for Inequalities Caution!When you multiply by a negative number… …the symbol CHANGES YES! -x > 2 5 (-5 )-x > 2(-5) 1 5 x < -10
- 14. Solving One-Step Solving One-Step Inequalities Inequalities Let’stry some on our own …… ready?
- 15. Solving One-Step Solving One-Step Inequalities#1 Inequalities #1 7 6 x
- 16. Solving One-Step Solving One-Step Inequalities#2 Inequalities #2 5 3 x
- 17. Solving One-Step Solving One-Step Inequalities#3 Inequalities #3 15 3 x
- 18. Solving One-Step Solving One-Step Inequalities#4 Inequalities #4 5 9 x
- 19. Solving One-Step Solving One-Step Inequalities#5 Inequalities #5 3 2 1 x
- 20. Solving One-Step Solving One-Step Inequalities#6 Inequalities #6 7 3 x
- 21. Solving One-Step Solving One-Step Inequalities#7 Inequalities #7 7 5 x
- 22. Solving One-Step Solving One-Step Inequalities#8 Inequalities #8 5 3 x
- 23. Solving 2-Step Inequalities Follow same steps used to solve 2-step equations: 3x + 4 < 13 - 4 -4 3x < 9 3 3 x < 3
- 24. Practice -2x +5 > 15 14 > x + 4 -4 17 – 3 x < 41 x < 7 -5
- 25. Time to Practice! Solve: 6x – 8 > 22
- 26. Practice Problem 1 −4− 5v < −29
- 27. Practice Problem 2 −1+ 4x ≤ 31
- 28. Practice Problem 3 −2+ r > −1 9
- 29. Practice Problem 4 −52< 8 + 5k -8 -8 -60 < 5K 5 5 (see next screen to continue)
- 30. Practice Problem 4– When Variable is on the Right Side you have to switch and reverse the symbol -60 < 5K 5 5 (see next screen to continue) 12 < K So K > 12
- 31. Practice Problem 5 8− 7n > −20
- 32. Practice Problem 6 −9≥ −8 + v −6