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Wednesday, September 4 th Please complete the warm up 

Wednesday, September 4 th Please complete the warm up . Solve: -(x+3)=5 + 2(4x-20) Solve:. Joke of the Day. How do equations get into shape?!?! They do multi-step aerobics. Homework Answers. Around the World. Fraction Coefficients. Don’t forget to: FLIP The coefficient. 1. 2.

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Wednesday, September 4 th Please complete the warm up 

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  1. Wednesday, September 4th Please complete the warm up  Solve: -(x+3)=5 + 2(4x-20) Solve:

  2. Joke of the Day How do equations get into shape?!?! They do multi-step aerobics

  3. Homework Answers Around the World

  4. Fraction Coefficients Don’t forget to: FLIP The coefficient 1. 2. 3.

  5. What Did the Superman Do Wrong?!?! -(x – 4) = -3x - 7 + 5x -x – 4 = 8x + 7 -4=7x + 7 -11 = 7x -11/7 = x

  6. What Did the Sponge Bob Do Wrong?!?!

  7. Helpful Hint Equations are often easier to solve when the variable has a positive coefficient. Keep this in mind when deciding on which side to "collect" variable terms.

  8. Let’s Practice What would I do to keep the coefficient Positive? • 7a – 17 = 4a + 1 • 2b – 5 = 8b + 1 • 4x – 2 = 3x + 4 • 2x -5 = 4x – 1 • 5x + 2 = 3x You’ve got to Practice!

  9. Let’s get warmed Up! • –4 + 7x = 3 • 6 – 7(a + 1) = –3(2 – a

  10. +36 +36 + 2a +2a Challenge Problem 4 – 6a + 4a = –1 – 5(7 – 2a) Distribute –5 to the expression in parentheses. 4 – 6a + 4a = –1 –5(7 – 2a) 4 – 6a + 4a = –1 –5(7) –5(–2a) 4 – 6a + 4a = –1 – 35 + 10a Combine like terms. 4 – 2a = –36 + 10a Since –36 is added to 10a, add 36 to both sides. 40 – 2a = 10a To collect the variable terms on one side, add 2a to both sides. 40 = 12a

  11. Any Questions before we go further…..

  12. Graphing and Solving Inequalities

  13. < > ≥ ≤ ≠ A<B A >B A ≤ B A ≥B A ≠ B A is greater than or equal to B. A is less than or equal toB. Ais less thanB. A is greater thanB. A is not equal toB. Vocabulary 1. An inequalityis a statement that two quantities are not equal. The quantities are compared by using the following signs: 2. A solution of an inequalityis any value that makes the inequality true.

  14. Graphing Inequalities An inequality like x < 6has too many solutions to list. You can use a graph on a number line to show all the solutions. • The solutions are shaded and an arrow shows that the solutions continue past those shown on the graph. • To show that an endpoint is a solution, draw a solid circle at the number. • To show an endpoint is not a solution, draw an empty circle.

  15. Don't Shade Shade • < Less than Example: x<4 • > Greater than Example: x > 5 • ≤ Less than OR equal to Example: x ≤5 • ≥ Greater than OR equal to Example: x ≥6 o o To Shade or Not to Shade

  16. Words Example • D: Draw a number line and a circle at the endpoint • I: Include? To shade or not to shade! • S: Shade in the correct direction • C: Check: substitute a value on the solution and check to see if it’s true x <4 D: I: S: Check: Is -5 less than 4? o Steps to Graphing Inequalities: DISC

  17. Draw a solid circle at . Shade all the numbers greater than and draw an arrow pointing to the right. 0 2 3 3 – t < 5(–1 + 3) 1 t < 5(2) t < 10 0 –8 –6 –4 –2 2 4 6 8 10 12 Example of Graphing Inequalities Graph each inequality. A. m ≥ B. t < 5(–1 + 3) Simplify. Draw an empty circle at 10. Shade all the numbers less than 10 and draw an arrow pointing to the left.

  18. Page 31 IMN Reading Math • “No more than” means “less than or equal to.” • “At least” means “greater than or equal to”.

  19. Guess What?!?! Solving one-step inequalities is much like solving one-step equations. To solve an inequality, you need to isolate the variable using the properties of inequality and inverse operations.

  20. –12 –12 –8 –2 –10 –6 –4 0 2 4 6 8 10 Using Addition and Subtraction to Solve Inequalities Solve the inequality and graph the solutions. x + 12 < 20 x + 12 < 20 Since 12 is added to x, subtract 12 from both sides to undo the addition. x + 0 < 8 x < 8 Draw an empty circle at 8. Shade all numbers less than 8 and draw an arrow pointing to the left.

  21. 7x > –42 > –8 –2 –10 –6 –4 0 2 4 6 8 10 Multiplying or Dividing by a Positive Number Solve the inequality and graph the solutions. 7x > –42 Since x is multiplied by 7, divide both sides by 7 to undo the multiplication. 1x > –6 x > –6

  22. Since r is multiplied by , multiply both sides by the reciprocal of . 0 2 4 6 8 10 14 20 12 18 16 Multiplying or Dividing by a Positive Number Solve the inequality and graph the solutions. r < 16

  23. MOST IMPORTANT PART OF TODAY!!!!!!!!!!

  24. If you multiply or divide both sides of an inequality by a negative number, the resulting inequality is not a true statement. You need to reverse the inequality symbolto make the statement true.

  25. –7 –14 –12 –8 –2 –10 –6 –4 0 2 4 6 Multiplying or Dividing by a Negative Number Solve the inequality and graph the solutions. –12x > 84 Since x is multiplied by –12, divide both sides by –12. Change > to <. x < –7

  26. Caution! Do not change the direction of the inequality symbol just because you see a negative sign. For example, you do not change the symbol when solving 4x < –24.

  27. 45 + 2b > 61 –45 –45 b > 8 0 2 4 6 8 10 14 20 12 18 16 Solving Multi-Step Inequalities Page 5 IMN #1 Solve the inequality and graph the solutions. 45 + 2b > 61 Since 45 is added to 2b, subtract 45 from both sides to undo the addition. 2b > 16 Since b is multiplied by 2, divide both sides by 2 to undo the multiplication.

  28. 8 – 3y ≥ 29 –8 –8 –7 –8 –10 –6 –4 0 2 4 6 8 10 –2 Keep Practicing! #2 8 – 3y ≥ 29 Since 8 is added to –3y, subtract 8 from both sides to undo the addition. –3y ≥21 Since y is multiplied by –3, divide both sides by –3 to undo the multiplication. Change ≥ to ≤. y ≤ –7

  29. –12 ≥ 3x + 6 – 6 – 6 –8 –10 –6 –4 0 2 4 6 8 10 –2 Make sure variable is on the left!!! #3 –12 ≥ 3x + 6 Since 6 is added to 3x, subtract 6 from both sides to undo the addition. –18 ≥ 3x Since x is multiplied by 3, divide both sides by 3 to undo the multiplication. –6 ≥ x x≤-6

  30. x + 5 < –6 –5 –5 –11 –20 –16 –12 –8 –4 0 You try!!! #4 Since x is divided by –2, multiply both sides by –2 to undo the division. Change > to <. Since 5 is added to x, subtract 5 from both sides to undo the addition. x < –11

  31. – 11 –11 10 –8 –10 –6 –4 0 2 4 6 8 –2 #5 You try!!! 3 + 2(x + 4) > 3 Take it step by step Distribute 2 on the left side. 3 + 2(x + 4) > 3 3 + 2x + 8 > 3 Combine like terms. 2x + 11 > 3 Since 11 is added to 2x, subtract 11 from both sides to undo the addition. 2x > –8 Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. x > –4

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