Use variables and appropriate operations to write inequality. Inequalities Use variables and appropriate operations to write inequality.

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Preview Warm Up California Standards Lesson Presentation

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 – 3m x 4 1 +

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

Vocabulary inequality algebraic inequality solution set

Inequality Symbols < less than > greater than Notice open circles

Inequality Symbols ≤ less than or equal to ≥ greater than or equal to Notice colored in circles

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

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

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

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

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

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.

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

Additional Example 3: Graphing Inequalities Graph each inequality. 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. –3 –2 –1 0 1 2 3 12 B. z ≥ –2 Draw a closed circle at –2 and all values of z greater than -2 . So shade to the right of –2 . 1 2 –3 –2 –1 0 1 2 3

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

A compound inequality is the result of combining two inequalities 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

Additional Example 4: Writing Compound Inequalities Write a compound inequality for each statement. 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

Check It Out! Example 4 Write a compound inequality for each statement. 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

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. p < 150 f ≥ 20 n – 5 ≤ 16 15z > 100

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