Do Now 12/14/09Do Now 12/14/09

Take out HW from Friday.Take out HW from Friday.– Text p. 359, #4-14 even 22-36 evenText p. 359, #4-14 even 22-36 even

Copy HW in your planner.Copy HW in your planner.– Text p. 366, #16-32 even, 36 & 40. Text p. 366, #16-32 even, 36 & 40.

Complete the activity on page 362 in your Complete the activity on page 362 in your textbook. Read through the “Explore” steps #1-textbook. Read through the “Explore” steps #1-3. Then complete the “Draw Conclusions” 3. Then complete the “Draw Conclusions” problems #1-8.problems #1-8.

HomeworkHomeworkText p. 359, #4-14 even 22-36 evenText p. 359, #4-14 even 22-36 even

4) a ≥ 164) a ≥ 166) x ≤ -46) x ≤ -48) x > 48) x > 410) x < 110) x < 112) m ≥ -4¼ 12) m ≥ -4¼ 14) v > -15.814) v > -15.822) 8 should have been subtracted from both sides of the inequality. x < -11.22) 8 should have been subtracted from both sides of the inequality. x < -11.24) 11 + m > -23; m > -3424) 11 + m > -23; m > -3426) c – 13 < -19; c < -626) c – 13 < -19; c < -628) x ≤ 3.328) x ≤ 3.330) x < 17.730) x < 17.732) at least 33 goals32) at least 33 goals34) C34) C36) 2 axles: w ≤ 19,800, 3 axles: w ≤ 39,800, 4 axles: w ≤ 54,800, 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 ActivityInvestigating Algebra Activity“Inequalities with Negative Coefficients”“Inequalities with Negative Coefficients”

Complete the activity on page 362 in your Complete the activity on page 362 in your textbook. Read through the “Explore” textbook. Read through the “Explore” steps #1-3. Then complete the “Draw steps #1-3. Then complete the “Draw Conclusions” problems #1-8. Conclusions” problems #1-8.

INEQUALITIESINEQUALITIES – – mathematical sentence formed by mathematical sentence formed by placing a <, ≤, >, or ≥ between two placing a <, ≤, >, or ≥ between two expressions. expressions.

y² – 8 < 12 y² – 8 < 12

13 * 22 13 * 22 ≥≥ 14 - z14 - z

11 - a 11 - a ≤≤ 121121

5 ÷ x > 30

5 ÷ x > 30

Section 6.2Section 6.2“Solve Inequalities Using Multiplication and “Solve Inequalities Using Multiplication and

Division”Division”

On a number line, the On a number line, the GRAPH OF AN GRAPH OF AN INEQUALITYINEQUALITY in one variable is the set of in one variable is the set of points that represent all solutions of the points that represent all solutions of the inequality.inequality.

Graph x < 3Graph x < 3

00 11-1-1 22-2-2 33

Graph x ≥ -1Graph x ≥ -1

00 11-1-1 22-2-2 33

““Less than” and “greaterLess than” and “greaterthan” are representedthan” are representedwith an open circle.with an open circle.

““Less than or equal to” Less than or equal to” and “greater than or equaland “greater than or equalto” are represented with to” are represented with closed circle.closed circle.

Write original inequalityWrite original inequality..

Multiply each side byMultiply each side by 4.4.

Simplify.Simplify.

ANSWERANSWER

The solutions are all real numbers The solutions are all real numbers less thanless than 2020.. Check by substituting Check by substituting a number less thana number less than 20 20 in the in the original inequality.original inequality.

. Graph your solution.. Graph your solution.xx 44

<< 55SolveSolve

xx 44

<< 5.5.

xx 44

<<44 44 55

x x < 20< 20

Write original inequalityWrite original inequality..

Multiply each side byMultiply each side by 8.8.

SimplifySimplify..

The solutions are all real numbers less than The solutions are all real numbers less than are equalare equal toto –– 16. 16. Check by substituting a Check by substituting a number less than number less than –– 16 16 in the original inequalityin the original inequality..

Graph your solution.Graph your solution.mm 88

≤≤ -2-2SolveSolve

mm 88

≤ –≤ – 22

m m ≤≤ – – 16 16

mm 88

88 88≤ –≤ – 22

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

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

Write original inequalityWrite original inequality..

Multiply each side byMultiply each side by –– 7. 7. Reverse inequality symbolReverse inequality symbol..

SimplifySimplify..

ANSWERANSWER

The solutions are all real numbers greater than The solutions are all real numbers greater than –– 11.2. 11.2. Check by substituting a number greater than Check by substituting a number greater than –– 11.2 11.2 in the in the original inequalityoriginal inequality..

< < 1.61.6

mm–– 77

SolveSolve

m > –m > – 11.2 11.2

mm–– 77 < < 1.61.6

–– 77 1.61.6> > –– 7 7mm

–– 77

Write original inequalityWrite original inequality..

Divide each side by Divide each side by –3.–3. Reverse Reverseinequality symbolinequality symbol..

SimplifySimplify..

––33x x >> 2424..SolveSolve

––33x x >> 2424..

––33xx––33

<< 2424––33

x x < – 8< – 8

Solve a real-world problemSolve 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 < 80r 6000 B <– 80r 6000 C >– 80r 6000 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 problemSolve a real-world problem

What are the possible hourly rates that the student can afford to pay for training?

Write inequality.Write inequality.

80r80

≤ 600080

Divide each side by Divide each side by 80.80.

r ≤ 75 Simplify.Simplify.

The student can afford to pay at most $75 per hour for training.

80 r ≤ 6000

Algebra in “Real-Life!”Algebra in “Real-Life!”

In your groups, complete the “real-life” In your groups, complete the “real-life” activity. activity. – Interdisciplinary Application “Bald Eagles”Interdisciplinary Application “Bald Eagles”

Algebra in “Real-Life!”Algebra in “Real-Life!”

In your groups, complete the two “real-life” In your groups, complete the two “real-life” activities. activities. – Interdisciplinary Application “Bald Eagles”Interdisciplinary Application “Bald Eagles”

1) y = 393x + 14,3241) y = 393x + 14,3242) graph2) graph3) approximately 18,2543) approximately 18,2544) habitat loss, less people counting 4) habitat loss, less people counting 5) y = 512.5x + 13,6985) y = 512.5x + 13,6986) graph6) graph7) approximately 18,8807) approximately 18,880

2424

NJASK7 PrepNJASK7 Prep

HomeworkHomework

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