Do Now 1/3/11 Copy HW in your planner. Copy HW in your planner. –Text p. 141, #12-32 evens Be ready to copy POTW #6. Be ready to copy POTW #6.

Objective SWBAT solve simple inequalities and use inequalities to solve real-life problems In your notebook, 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? In your notebook, 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?

Section 3.4, “ Solving Inequalities Using Addition and Subtraction” Section 3.4, “ Solving Inequalities Using Addition and Subtraction” INEQUALITIES – INEQUALITIES – mathematical sentence formed by placing a, or ≥ between two expressions. mathematical sentence formed by placing a, or ≥ between two expressions. y – 8 < 12 y – 8 < ≥ 14 - z 13 ≥ 14 - z 11 + a ≤ a ≤ 121 x +8 > 30 x +8 > 30

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. 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 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.

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.

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 > – 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. Solve x – 5 > -3.5 Graph your solution Graph your solution

p – 9.2 < – p < 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. Solve p – 9.2 < -5 Graph your solution Graph your solution

9 ≥ x + 7 Write original inequality. – 7 – 7 – 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 Graph your solution

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

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

Homework Text p. 141, #12-38 even