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Do Now 12/16/09

Do Now 12/16/09. Take out HW from Monday and Tuesday. Text p. 366, #16-32 even, 36 & 40 Text p.368, #1-10 Copy HW in your planner. Text p. 372, #10-24 even, 30-34 even, 38, 40. 16) d ≥ -37.2 18) k ≤ 0.49 20) x ≥ 37.5 22) y ≤ 45 24) p ≤ -0.38 26) t < 0.61

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Do Now 12/16/09

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  1. Do Now 12/16/09 • Take out HW from Monday and Tuesday. • Text p. 366, #16-32 even, 36 & 40 • Text p.368, #1-10 • Copy HW in your planner. • Text p. 372, #10-24 even, 30-34 even, 38, 40

  2. 16) d ≥ -37.2 18) k ≤ 0.49 20) x ≥ 37.5 22) y ≤ 45 24) p ≤ -0.38 26) t < 0.61 28) The inequality sign was not reversed when dividing by -15. x < -3. 30) 8x > 50; x > 25/4 32) v/-9 < -18; v > 162 36) at most 5 CDs 40) d < 18(0.75); d < 13.5 miles HomeworkText p. 366, #16-32 even, 36 & 40

  3. Punchline worksheets “How Can you Tell Van Winkle’s Trousers?” “How Did the Turtle Call for HELP When His Car Broke Down?” There’s a rip in them He Used His Shell Phone

  4. 1) x ≥ -13 2) y < 8 3) v ≥ -3 4) w > 13 5) r < 8 6) s > -31 7) m ≤ -13 8) n < 28 9) c ≤ -48 10) at least 50 minutes Homework Text p.368, #1-10

  5. Section 6.3“Solve Multi-Step Inequalities” INEQUALITIES – mathematical sentence formed by placing a <, ≤, >, or ≥ between two expressions. 13 * 22 ≥14 - z 2y – 8 < 12 5c + 14 > 30 w/11 - 10 ≤121

  6. Section 6.3“Solve Multi-Step Inequalities” The steps for solving two-step and multi-step equations can be applied to linear inequalities.

  7. REMEMBER!!!!! Multiplying and/or dividing each side of an inequality by a NEGATIVE number only produces an equivalent inequality IF the inequality sign is REVERSED!!

  8. Solve 3x– 7 < 8.Graph your solution. ANSWER The solutions are all real numbers less than 5. Check by substituting a number less than 5 in the original inequality. 3x– 7 < 8 Write original inequality. 3x< 15 Add 7 to each side. x< 5 Divide each side by 3.

  9. Solve –0.6(x– 5)<15 – –0.6(x–5)<15 – –0.6x+ 3 <15 – –0.6x<12 – ANSWER – The solutions are all real numbers greater than equal -20. Check by substituting a number more than -20 in the original inequality. Divide each side by 0.6. Reverse inequality symbol. x > –20 – Write original inequality. Distributive property Subtract 3 from each side.

  10. –1 –1 ( p –12) > –2 4 4 ( p –12) > -2 ANSWER The solutions are all real numbers greater than 20. Check by substituting a number greater than 20. Write original inequality. – ¼ p + 3 > -2 Distributive property. -¼ p > –5 p < 20

  11. Solve 6x– 7 > 2x+17.Graph your solution. ANSWER The solutions are all real numbers greater than 6. 6x– 7 > 2x+17 Write original inequality. 6x > 2x+24 Add 7 to each side. 4x > 24 Subtract 2xfrom each side. x > 6 Divide each side by 4.

  12. 14x+ 5 < 7(2x –3) There are no solutions because 5<–21is false. Solve: 14x+ 5 < 7(2x –3) Write original inequality. 14x+ 5 < 14x –21 Distributive property 5 < –21 Subtract 14xfrom each side. **HINT** If an inequality is equivalent to an inequality that is false, such as 5 < -21, then the solution of the inequality has NO SOLUTION.

  13. All real numbers are solutions because –1 > –6 is true. 12x –1 > 6(2x – 1) 12x –1 > 6(2x – 1) Write original inequality. 12x –1 > 12x – 6 Distributive property –1 > –6 Subtract 12xfrom each side. **HINT** If an inequality is equivalent to an inequality that is true, such as -1 > -6, then the solutions of the inequality are ALL REAL NUMBERS .

  14. Graphs of “No Solution” and “All Real Numbers” • “No Solution” • “All Real Numbers”

  15. Amount ofgasoline (gallons) Maximumamount (dollars) Price ofcar wash (dollars) Price ofgasoline (dollars/gallon) + • < g < 1.99 + 8 20 – Car Wash Use the sign shown. A gas station charges $.10 less per gallon of gasoline if a customer also gets a car wash. What are the possible amounts (in gallons) of gasoline that you can buy if you also get a car wash and can spend at most $20? Because you are getting a car wash, you will pay $2.09–2 $.10 = $1.99 per gallon of gasoline. Let gbe the amount (in gallons) of gasoline that you buy. STEP 1 Write a verbal model. Then write an inequality.

  16. STEP2 You can buy up to slightly more than 6 gallons of gasoline. Solve the inequality. 1.99g +8 ≤ 20 Write inequality. Subtract8from each side. 1.99g ≤ 12 Divide each side by 1.99. g ≤ 6.03015. . . CHECK You can use a table to check the reasonableness of your answer.The table shows that you will pay $19.94 for exactly 6 gallons of gasoline. Because $19.94 is less than $20, it is reasonable to conclude that you can buy slightly more than 6 gallons of gasoline.

  17. Homework • Text p. 372, #10-24 even, 30-34 even, 38, 40

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