The document provides examples for writing inequalities from word phrases, writing compound inequalities from statements, and graphing inequalities on a number line. It includes examples such as "There are at least 35 people in the gym" which can be written as the inequality p ≥ 35. It also demonstrates how to graph inequalities by shading the appropriate areas of a number line based on whether the inequality symbol is <, ≤, >, or ≥.

1. Warm Up California Standards Lesson Presentation Preview

2. Warm Up Order each set of integers from least to greatest. 1. –7, 8, –9 2. –2, 2, 0,  1 3. –11,  13,  10 Write an algebraic expression for each word phrase. 4. 2 less than g 5. 5 minus the product of 3 and m 6. 1 more than the quotient of x and 4 – 9, –7, 8 – 2, –1, 0, 2 – 13, –11, –10 g – 2 5 – 3 m 1 + x 4

3. AF1.1 Use variables and appropriate operators to write an expression, an equation, an inequality, or a system of equations or inequalities that represents a verbal description (e.g., three less than a number, half as large as area A). California Standards

4. Vocabulary inequality algebraic inequality solution set

5. An inequality compares two expressions using <, >,  , or  . is less than is greater than is greater than or equal to is less than or equal to Fewer than, below More than, above At most, no more than At least, no less than An inequality that contains a variable is an algebraic inequality . ≥ ≤ > < Word Phrases Meaning Symbol

6. Write an inequality for each situation. Additional Example 1: Translating Word Phrases into Inequalities A. There are at least 35 people in the gym. p ≥ 35 B. The carton holds at most 12 eggs. e ≤ 12 “ At least” means greater than or equal to. “ At most” means less than or equal to. Let p = the number of people in the gym. Let e = the number of eggs the carton hold.

7. Write an inequality for each situation. Check It Out! Example 1 A. There are at most 10 gallons of gas in the tank. g ≤ 10 B. There are fewer than 10 yards of fabric left. y < 10 “ At most” means less than or equal to. “ Fewer than” means less than. Let g = the number of gallons of gas. Let y = the yards of fabric.

8. Write an inequality for each statement. Additional Example 2: Writing Inequalities A. A number m multiplied by 5 is less than 25. 5 m < 25 B. The sum of a number y and 16 is no more than 100. y + 16 ≤ 100 m  5 < 25 The sum of a number y and 16 is no more than 100 A number m multiplied by 5 is less than 25. y + 16 ≤ 100

9. Write an inequality for each statement. Check It Out! Example 2 A. A number y plus 14 is greater than 21. y + 14 > 21 B. A number t increased by 7 is more than 11 t + 7 > 11 y + 14 > 21 A number t is increased by 7 is more than 11 A number y plus 14 is greater than 21. t + 7 > 11

10. A solution of an inequality is any value of the variable that makes the inequality true. All of the solutions of an inequality are called the solution set . You can graph the solution set on a number line. The symbols < and > indicate an open circle.

11. This open circle shows that 5 is not a solution. a > 5 The symbols ≤ and ≥ indicate a closed circle. This closed circle shows that 3 is a solution. b ≤ 3

12. Graph each inequality. – 3 –2 –1 0 1 2 3 A. –1 > y Draw an open circle at –1. The solutions are all values of y less than –1, so shade the line to the left of –1. B. z ≥ –2 – 3 –2 –1 0 1 2 3 Additional Example 3: Graphing Inequalities 1 2 Draw a closed circle at –2 and all values of z greater than  2 . So shade to the right of –2 . 1 2 1 2 1 2

13. Graph each inequality. – 3 –2 –1 0 1 2 3 A. n < 3 B. a ≥ –4 – 6 –4 –2 0 2 4 6 Check It Out! Example 3 Draw an open circle at 3. The solutions are all values of n less than 3, so shade the line to the left of 3. Draw a closed circle at –4. The solutions are all values greater than –4, so shade to the right of –4.

14. A compound inequality is the result of combining two inequalities. The words and and or are used to describe how the two parts are related. The compound inequality –2 < y and y < 4 can be written as –2 < y < 4. Writing Math

15. Write a compound inequality for each statement. Additional Example 4: Writing Compound Inequalities A. A number x is both less than 4 and greater than or equal to –2.5. – 2.5 ≤ x < 4 B. A number t is either greater than –1 or less than or equal to –7. t > –1 or t ≤ –7

16. Write a compound inequality for each statement. Check It Out! Example 4 A. A number t is both greater than 9 and less than or equal to 18.5 9 < t  18.5 B. A number y is either greater than –5 or less than or equal to –1. y > –5 or y ≤ –1

17. Lesson Quiz: Part I Write an inequality for each situation. 1. Fewer than 150 people bought tickets. 2. There are at least 20 finches in the cage. Write an inequality for each statement. 3. A number n decreased by 5 is at most 16. 4. The product of 15 and a number z is greater than 100. f ≥ 20 p < 150 n – 5 ≤ 16 15 z > 100

18. Lesson Quiz: Part II 6. –3 < y Graph each inequality. 5. m ≤ 1 0 º 1 2 3 – 1 – 2 3 – – – – 0 1 2 3 1 2 3