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

Homework Text p. 366, #16-32 even, 36 & 40  16) d ≥  18) k ≤ 0.49  20) x ≥ 37.5  22) y ≤ 45  24) p ≤  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/  36) at most 5 CDs  40) d < 18(0.75); d < 13.5 miles

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Homework Text p.368, #1-10  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

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

Solving Multi-Step Inequalities STEP 1- Use distributive property and combine like terms. STEP 2- Collect variables on one side of the inequality. STEP 3- “Undo” addition and/or subtraction. STEP 4- “Undo” multiplication and/or division. STEP 5- Solve for the variable. STEP 6- Check your work. The steps for solving two-step and multi-step equations can be applied to linear inequalities.

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

3x – 7 < 8 Write original inequality. 3x < 15 Add 7 to each side. x < 5 x < 5 x < 5 x < 5 Divide each side by 3. 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. Graph your solution. Solve

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

Write original inequality. Distributive property. ANSWER The solutions are all real numbers greater than 20. Check by substituting a number greater than 20. –14 ( p –12) > -2 – ¼ p + 3 > -2 -¼ p > –5 p < 20 –14 ( p –12) > –2

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

14x + 5 < 7(2x – 3) Write original inequality. 14x + 5 < 14x – 21 Distributive property 5 < – 21 Subtract 14x from each side. There are no solutions because 5 < – 21 is false. Solve: 14x + 5 < 7(2x – 3) Solve: 14x + 5 < 7(2x – 3) **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.

12x – 1 > 6(2x – 1) 12x – 1 > 6(2x – 1) Write original inequality. Distributive property Subtract 12x from each side. 12x – 1 > 12x – 6 – 1 > – 6 All real numbers are solutions because – 1 > – 6 is true. 12x – 1 > 6(2x – 1) 12x – 1 > 6(2x – 1) **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.

Graphs of “No Solution” and “All Real Numbers”  “No Solution”  “All Real Numbers”

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? Car Wash STEP 1 Write a verbal model. Then write an inequality. Because you are getting a car wash, you will pay $2.09 – 2 $.10 = $1.99 per gallon of gasoline. Let g be the amount (in gallons) of gasoline that you buy g 820 < – Price of gasoline (dollars/gallon) Amount of gasoline (gallons) Price of car wash (dollars) Maximum amount (dollars) + <

STEP 2 Solve the inequality. Write inequality. Subtract 8 from each side. 1.99g ≤ g + 8 ≤ 20 Divide each side by g ≤ You can buy up to slightly more than 6 gallons of gasoline. 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. Gasoline(gal) Total amount spent (dollars)

Homework  Text p. 372, #10-24 even, even, 38, 40