Do Now 12/14/09 Take out HW from Friday. –Text p. 359, #4-14 even even Copy HW in your planner. –Text p. 366, #16-32 even, 36 & 40. Complete the activity on page 362 in your textbook. Read through the “Explore” steps #1- 3. Then complete the “Draw Conclusions” problems #1-8.

Homework Text p. 359, #4-14 even even 4) a ≥ 16 6) x ≤ -4 8) x > 4 10) x < 1 12) m ≥ -4¼ 14) v > ) 8 should have been subtracted from both sides of the inequality. x < ) 11 + m > -23; m > ) c – 13 < -19; c < -6 28) x ≤ ) x < ) at least 33 goals 34) C 36) 2 axles: w ≤ 19,800, 3 axles: w ≤ 39,800, 4 axles: w ≤ 54,800, 5 axles: w ≤ 65,800. No, the total weight, 34,200 would exceed the 5 axles: w ≤ 65,800. No, the total weight, 34,200 would exceed the maximum weight allowed, 34,000 pounds. maximum weight allowed, 34,000 pounds.

Investigating Algebra Activity “Inequalities with Negative Coefficients” Complete the activity on page 362 in your textbook. Read through the “Explore” steps #1-3. Then complete the “Draw Conclusions” problems #1-8.

INEQUALITIES – INEQUALITIES – mathematical sentence formed by placing a, or ≥ between two expressions. mathematical sentence formed by placing a, or ≥ between two expressions. y² – 8 < 12 y² – 8 < * 22 ≥ 14 - z 13 * 22 ≥ 14 - z 11 - a ≤ a ≤ ÷ x > 30 5 ÷ x > 30 Section 6.2 “Solve Inequalities Using Multiplication and Division”

On a number line, the GRAPH OF AN INEQUALITY in one variable is the set of points that represent all solutions of the inequality. Graph x < Graph x ≥ “Less than” and “greater than” are represented with an open circle. “Less than or equal to” and “greater than or equal to” are represented with closed circle.

Write original inequality. Multiply each side by 4. Simplify.ANSWER The solutions are all real numbers less than 20. Check by substituting a number less than 20 in the original inequality.. Graph your solution. x 4 < 5 Solve x 4 < x 4 < x < 20

Write original inequality. Multiply each side by 8. Simplify. The solutions are all real numbers less than are equal to – 16. Check by substituting a number less than – 16 in the original inequality. Graph your solution. Graph your solution.m 8 ≤ Solve m 8 ≤ – 2 m ≤ – 16 m ≤ – 2

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!! Solve Inequalities When Multiplying and Dividing by a NEGATIVE”

Write original inequality. Multiply each side by – 7. Reverse inequality symbol. Simplify. ANSWER The solutions are all real numbers greater than – Check by substituting a number greater than – 11.2 in the original inequality. < 1.6 < 1.6m – 7– 7– 7– 7 Solve m > – 11.2 m – 7– 7– 7– 7 < 1.6 – 7– 7– 7– > – 7 m – 7– 7– 7– 7

Write original inequality. Divide each side by –3. Reverse inequality symbol. Simplify. –3x > 24. Solve –3x –3 < 24 –3 x < – 8

Solve a real-world problem SOLUTION A student pilot plans to spend 80 hours on flight training to earn a private license. The student has saved $6000 for training. Which inequality can you use to find the possible hourly rates r that the student can afford to pay for training ? 80r 6000 A < B < – C > – D > The total cost of training can be at most the amount of money that the student has saved. Write a verbal model for the situation. Then write an inequality. The correct answer is B. A DCB 80 r < – 6000

Solve a real-world problem What are the possible hourly rates that the student can afford to pay for training ? Write inequality. 80r 80 ≤ Divide each side by 80. r ≤ 75 Simplify. The student can afford to pay at most $75 per hour for training. 80 r ≤ 6000

Algebra in “Real-Life!” In your groups, complete the “real-life” activity. –Interdisciplinary Application “Bald Eagles”

Algebra in “Real-Life!” In your groups, complete the two “real-life” activities. –Interdisciplinary Application “Bald Eagles” 1) y = 393x + 14,324 2) graph 3) approximately 18,254 4) habitat loss, less people counting 5) y = 512.5x + 13,698 6) graph 7) approximately 18,880

24 NJASK7 Prep

Homework Text p. 366, #16-32 even, 36 & 40