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Section 3-1 Inequalities and their Graphs SPI 22N: identify the graphical representation of the solution to a one variable inequality on a number line Objectives: Identify solutions of inequalities Graph and write inequalities Vocabulary Solution of an inequality: any number that makes the equation true. Example: For the inequality x > 3, all numbers that are less than 3 make the inequality true. Remember the Signs of Inequality > Greater than < Less than = Equal to Less than and equal to Greater than and equal to

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Is each number a solution of x 5? > Yes, 5 5 is true. > No, –2 5 is not true. > Yes, 10 5 is true. > a. –2b. 10 c. 25 5 Is each number a solution of 3 + 2x < 8? a. –2b. 3 3 + 2x < 8 –2 is a solution. 3 + 2(–2) < 8Substitute for x. 3 – 4 < 8Simplify. –1 < 8 Compare. 3 + 2x < 8 3 is not a solution. 3 + 2(3) < 8 Substitute for x. 3 + 6 < 8 Simplify. 9 < 8Compare. Practice Understanding Inequalities

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a. Graph d < 3. b. Graph –3 ≥ g. The solutions of d < 3 are all the points to the left of 3. The solutions of –3 g are –3 and all the points to the left of –3. > An inequality may have more than one solution. Use the following symbols to graphically represent solutions to an inequality. Closed dot on a number line shows solution includes value Open dot on a number line shows solution does not include value Representing Inequalities on a Number Line

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x < 2Numbers less than 2 are graphed. x > –2 Numbers greater than –2 are graphed. x –3Numbers less than or equal to –3 are graphed. < > x Numbers greater than or equal to are graphed. 1212 1212 Writing Inequalities from Number Lines

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a. A speed that violates the law when the speed limit is 55 miles per hour. b. A job that pays at least \$500 a month. Let v = an illegal speed. The speed limit is 55, so v > 55. Let p = pay per month. The job pays \$500 or more, so p 500. > How would you graph the solutions to the above problems on a number line? Write an Inequality for each Situation

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Real World: Using Inequalities Suppose your school plans a musical. The goal is to have ticket sales of at least \$4000. Adult tickets are \$5.oo and student tickets are \$4.00. Let a represent the number of adult tickets and s represent the number of student tickets. Write an inequality that represents the school’s goal. 5a + 4s 4000

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