Do Now 12/11/09  Copy HW in your planner. Text p. 359, #4-14 even even. Text p. 359, #4-14 even even.  In your journal, answer the following question. Outside of the math classroom, where have you heard phrases such as “at least” or “no more than”? Give examples. How would you write the phrases mathematically?

Chapter 6 Preview “Solving and Graphing Linear Inequalities” (6.1) Solve Inequalities Using Addition and Subtraction (6.2) Solve Inequalities Using Multiplication and Division (6.3) Solve Multi-Step Inequalities (6.4) Solve Compound Inequalities (6.5) Solve Absolute Value Equations (6.6) Solve Absolute Value Inequalities (6.7) Graph Linear Inequalities in Two Variables Winter break

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 6.1 “Solve Inequalities Using Addition and Subtraction”

Writing Equations with Inequalities SymbolMeaning Key phrases = Is equal to The same as < Is less than Fewer than ≤ Is less than or equal to At most, no more than > Is greater than More than ≥ Is greater than or equal to At least, no less than

 On a number line, the GRAPH OF AN INEQUALITY 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 a closed circle

SOLUTION The highest temperature recorded in the United States was 134°F at Death Valley, California, in Use only this fact to write and graph an inequality that describes the temperatures in the United States. Let T represent a temperature (in degrees Fahrenheit) in the United States. The value of T must be less than or equal to 134. So, an inequality is T ≤ 134.

SOLUTION Write an inequality represented by the graph. The closed circle means that 8 is not a solution of the inequality. Because the arrow points to the left, all numbers less than 8 are solutions. ANSWER An inequality represented by the graph is x < 8.

SOLUTION The closed circle means that – 2.5 is a solution of the inequality. Because the arrow points to the right, all numbers greater than – 2.5 are solutions. ANSWER An inequality represented by the graph is x > – 2.5. Write an inequality represented by the graph.

Solving an Inequality… m + 4 < m < 8 m < 8 Isolate the variable! Get ‘m’ by itself. To get the ‘m’ by itself get rid of “adding 4.” Do the opposite. “Subtract 4.” Whatever you do to one side of the Inequality you must do the other side.

n - 5 ≥ n ≥ 11 n ≥ 11 Isolate the variable! Get ‘n’ by itself. To get the ‘n’ by itself get rid of “subtracting 5.” Do the opposite. “Add 5.” Whatever you do to one side of the inequality you must do the other side. Solving an Inequality…

x – 5 > – 3.5 x – > – x > 1.5 ANSWER The solutions are all real numbers greater than 1.5. Check by substituting a number greater than 1.5 for x in the original inequality. Write original inequality. Add 5 to each side. Simplify. x – 5 > – 3.5. Graph your solution. Solve

SOLUTION p – 9.2 < – 5 p – < – x < 4.2 Write original inequality. Add 9.2 to each side. Simplify. ANSWER The solutions are all real numbers less than 4.2. Check by substituting a number less than 4.2 for x in the original inequality. p – 9.2 < – 5. Graph your solution. Solve

9 ≥ x + 7 Write original inequality. 9 – 7 ≥ x + 7 – 7 Subtract 7 from each side. 2 ≥ x Simplify.ANSWER You can rewrite 2 ≥ x as x ≥ 2. The solutions are all real numbers less than or equal to 2. Solve 9  x + 7. Graph your solution. >

Write original inequality. Subtract 5.5 from each side. y > 0.5 Simplify. y > 6 y –5.5 > 6 –5.5 ANSWER You can rewrite The solutions are all real numbers greater than or equal to 0.5. SOLUTION Solve y > 6. Graph your solution. Solve y > 6. Graph your solution.

Solve a real-world problem LUGGAGE WEIGHTS You are checking a bag at an airport. Bags can weigh no more than 50 pounds. Your bag weighs 16.8 pounds. Find the possible weights w (in pounds) that you can add to the bag. SOLUTION Write a verbal model. Then write and solve an inequality. and solve an inequality w ≤ 50

16.8+ w 50 < Write inequality w – – 16.8 < Subtract 16.8 from each side. w ≤ 33.2 Simplify.ANSWER You can add no more than 33.2 pounds. Solve a real-world problem

Write and solve an inequality to find the possible values of x.  Perimeter ≤ 51.3 feet 14.2 ft 15.5 ft x ft x ≤ x ≤ 51.3 x ≤ 21.6

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

Algebra in “Real-Life!”  In your groups, complete the two “real-life” activities. Interdisciplinary Application “Bald Eagles” Interdisciplinary Application “Bald Eagles” 1) y = 393x + 14,3241) y = 393x + 14,324 2) graph2) graph 3) approximately 18,2543) approximately 18,254 4) habitat loss, less people counting4) habitat loss, less people counting 5) y = 512.5x + 13,6985) y = 512.5x + 13,698 6) graph6) graph 7) approximately 18,8807) approximately 18,880

Homework  Text p. 359, #4-14 even even 24 NJASK7 Prep

Practice Worksheet Form B #2-24 even  2) x > -2  4) x ≥ -7  6) x ≤ -1  8) n ≤ 12  10) m < 1  12) x ≤ -7.5  14) y < 4.8  16) d > 10.2  18) m – 3 ≥ 10; m ≥ 13  20) 85 > x – 63; x > 148  22) 17 hats or less  24) a) b). Yes, because 6392 > No, because 6385 is not > No, because 6377 is not > b). Yes, because 6392 > No, because 6385 is not > No, because 6377 is not > 6385.