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Graphing Equations and     Inequalities
PODDistribute1) 5(-6b + 6)2) -6(4r – 4)Combine Like Terms3) -30x + 30 + 5xSolve4) 5v + 5(-6v + 6) = -6(4v – 4)
5v + 5(-6v + 6) = -6(4v – 4)
Essential Questions:What is an inequality? How can I graph solutions of equations and inequalities on a number line?
Let’s Graph the Solution to an equation on a Number Line!Number lines are used to graph some solutions.                   ...
If we say that “a variable = a number”, that      is where we place the point on the                 number line!         ...
What Is The Difference Between Equalities And Inequalities?  The only difference is the number            of solutions!   ...
Inequality Symbols< Less Than                  x<5> Greater Than               x>5< Less Than OR Equal to      x<5> Gr...
If we say that x > 6,aren’t we stating that x can be  any amount greater than 6?    What are some examples??
How Do We View A Set OfSolutions On A Number Line?        Let’s find out!
When graphing inequalities, we must show whereto begin the set of solutions and where theycontinue on the number line.For ...
When graphing inequalities, we must show whereto begin the set of solutions and where theycontinue on the number line.For ...
If you noticed,      some number lines had filled in circles            and others did not.       What do you think was th...
The filled in circle shows that the     designated number is          included in the solution set.                This is...
The unfilled circle shows that the    designated number is not          included in the solution set.               This i...
Inequality Symbols< Less Than – Open Dot> Greater Than – Open Dot< Less Than OR Equal to – Closed Dot> Greater Than OR...
Solve and Graph the Following on YourPaper:A.) x – 1 > 5B.) 4 + n < -1C.) 5+ z > 10D.) -15 + r < -14
You should have drawn these solutions:  A.) x - 1 > 5      -5     -4    -3    -2 -1     0    1    2    3    4    5    6   ...
On your paper, solve and graphthe following:                     A. 5 + n = 9                     B. 19 + m > 5           ...
Now, Let’s Compare Equalities and Inequalities:       Equalities                  InequalitiesSolve by performing        ...
One more difference…                                     When you                  multiply When you                     ...
Vocabulary  •Number line  •Solution  •Inverse Operation  •Equality  •Inequality
Remember:Perform the   inverse operation      to solve for a variable!
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Graphing inequalities edmodo 10 16-2012

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Graphing inequalities edmodo 10 16-2012

  1. 1. Graphing Equations and Inequalities
  2. 2. PODDistribute1) 5(-6b + 6)2) -6(4r – 4)Combine Like Terms3) -30x + 30 + 5xSolve4) 5v + 5(-6v + 6) = -6(4v – 4)
  3. 3. 5v + 5(-6v + 6) = -6(4v – 4)
  4. 4. Essential Questions:What is an inequality? How can I graph solutions of equations and inequalities on a number line?
  5. 5. Let’s Graph the Solution to an equation on a Number Line!Number lines are used to graph some solutions. x + 3 = -1We already found the x + 3 -3 = -1 -3solution to this equation. x=-4 Now, what does it mean on a number line?
  6. 6. If we say that “a variable = a number”, that is where we place the point on the number line! Example: X = -3-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
  7. 7. What Is The Difference Between Equalities And Inequalities? The only difference is the number of solutions! •An equality gives one definite solution. •An inequality give a set of solutions!
  8. 8. Inequality Symbols< Less Than x<5> Greater Than x>5< Less Than OR Equal to x<5> Greater Than OR Equal to x>5
  9. 9. If we say that x > 6,aren’t we stating that x can be any amount greater than 6? What are some examples??
  10. 10. How Do We View A Set OfSolutions On A Number Line? Let’s find out!
  11. 11. When graphing inequalities, we must show whereto begin the set of solutions and where theycontinue on the number line.For example: r < 1 Use an open dot -2 -1 0 1 2
  12. 12. When graphing inequalities, we must show whereto begin the set of solutions and where theycontinue on the number line.For example: r > 1 Use a closed dot -2 -1 0 1 2
  13. 13. If you noticed, some number lines had filled in circles and others did not. What do you think was the reason?
  14. 14. The filled in circle shows that the designated number is included in the solution set. This is shown with < or >. X < -4
  15. 15. The unfilled circle shows that the designated number is not included in the solution set. This is shown with < or >. X < -4
  16. 16. Inequality Symbols< Less Than – Open Dot> Greater Than – Open Dot< Less Than OR Equal to – Closed Dot> Greater Than OR Equal to – Closed Dot
  17. 17. Solve and Graph the Following on YourPaper:A.) x – 1 > 5B.) 4 + n < -1C.) 5+ z > 10D.) -15 + r < -14
  18. 18. You should have drawn these solutions: A.) x - 1 > 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 B.) 4 + n < -1-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 C.) 5 + z > 10-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 D.) -15 + r < -14 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
  19. 19. On your paper, solve and graphthe following: A. 5 + n = 9 B. 19 + m > 5 C. -6 + b = 4 D. K - 17 < 14 E. 2d > 12
  20. 20. Now, Let’s Compare Equalities and Inequalities: Equalities InequalitiesSolve by performing Solve by performing the inverse operation the inverse operationOnly one definite A set of solutions solution The solution is shownThe solution is shown with a filled or unfilled with one filled circle on circle with a line or line a number line segment
  21. 21. One more difference…  When you multiply When you OR multiply Divide OR BY Divide A Positive BY the inequality A negative stays the same flipthe inequality
  22. 22. Vocabulary •Number line •Solution •Inverse Operation •Equality •Inequality
  23. 23. Remember:Perform the inverse operation to solve for a variable!

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