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1 Name Date Algebra I Data Sheet # Writing, Solving, and Graphing Inequalities- One-step, Multistep, and Compound How do you write, solve and graph inequalities? inequality set-builder notation Key Terms compound inequality inequality- Writing Inequalities < > less than fewer than less than or equal to at most no more than maximum greater than more than greater than or equal to at least no less than minimum Ex. 1 all real numbers p greater than or equal to 1.5 Ex. 2 the product of y and 6 is more than 12 Graphing Inequalities You can use a number line to show all of the solutions of an inequality. Draw a circle at the value included in the inequality. a. When the symbol is < or >, use an open dot on the graph. b. When the symbol is or, use a closed dot. Draw a heavy arrow pointing in the direction of all solutions that make the inequality true. 1 Mrs. N. Evans

2 Ex. 3 A person must be at least 35 years old to be elected President of the United States. Ex. 4 A light bulb can be no more than 75 watts to be safely used in this light fixture. Ex. 5 Write an inequality for each graph. a b c. Solving Inequalities To solve inequalities, undo operations same as you would with solving equations. Ex. 6 The hard drive on your computer has a capacity of 12 gigabytes (GB). You have used 85 GB. You want to save some home videos to your hard drive. What are the possible sizes of the home video collection you can save? Ex. 7 s 1 1 Ex. 8-6 > c 2 2 Mrs. N. Evans

3 When solving an inequality by multiplying or dividing, remember: If you multiply or divide by a positive number, If you multiply or divide by a negative number, the Ex. 9 Text messages cost $.15 each. You can spend no more than $1. How many text messages can you send? Ex. 1 9 < -3p Ex z > -33 Ex. 12 Ex. 13 In a community garden, you want to fence in a vegetable garden that is adjacent to your friend s garden. You have at most 42 feet of fence. What are the possible lengths of your garden? 3 Mrs. N. Evans

4 Ex. 14 3(h + 1) -9 Ex. 15 6n 1 > 3n + 8 Ex a 2(5 4a) Ex. 12 7m + 7 m < 6m 5 Ex. 13 The student council wants to rent a ballroom for the junior prom. The ballroom s rental rate is $15 for 3 hours and $125 for each additional half hour. Suppose the student council raises $2125. What is the maximum number of hours for which they can rent the ballroom? 4 Mrs. N. Evans

5 You can use set-builder notation to write the solutions of a linear inequality. set-builder notation- {x x 5} read as the set of all real numbers x, such that x is greater than or equal to 5 compound inequality- A compound inequality with the word and contains the overlap of the graphs of the two inequalities. 3 x < 7 read as x is greater than or equal to 3 and less than x x < x < 7 A compound inequality with the word or contains each graph of the two inequalities. x < -2 or x 1 read as x is less than -2 or greater than or equal to 1 x < -2 x 1 x < -2 or x 1 Ex. 14 Write and graph the compound inequality. a. All real numbers that are greater than -2 and less than 6 b. All real numbers that are less than or greater than or equal to 5 5 Mrs. N. Evans

6 A solution of a compound inequality involving and is any number that makes both inequalities true- solve by separating it into two inequalities or by working all three parts at the same time. Ex m 4 < -1 Ex. 16 To earn a B in your algebra course, you must achieve an unrounded test average between 84 and 86, inclusive. You scored 86, 85, and 8 on the first three tests of the grading period. What possible scores can you earn on the fourth and final test to earn a B in the course? A solution of a compound inequality involving or is any number that makes either inequality true- solve each inequality separately. Ex. 17 3t + 2 < -7 or -4t + 5 < 1 6 Mrs. N. Evans

7 Ex. 18 Write a compound inequality for each graph. a. b c Questions What did you learn? Answer the focus questions. Use an example if needed. Your Response/ Answer in Complete Sentences What do you need to say? Any special concerns or comments? What are you confused about? Please be honest. Remember that you are responsible for your education! 7 Mrs. N. Evans