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Solving One and Two-Step Inequalities #43 VOCABULARY An inequality is a statement that two quantities are not equal. The quantities are compared by using one of the following symbols: < > ≤ ≥ ≠ An inequality may contain a variable, as in x > 3. A solution of an equality is any value of the variable that makes the statement true. Example 1: Graphing Inequalities Graph the solutions of each inequality on a number line. A. t > 1 2 3 4 5 6 7 8 B. y 11 9 10 11 12 13 14 15 Example 2: Solving Inequalities with Addition or Subtraction Solve and graph each inequality. x–3≥5 –1 0 1 2 3 4 5 6 7 8 9 10 11 Example 3 Solve and graph each inequality. 5<x+3 1 2 3 4 5 6 7 Example 4: Solving Inequalities with Multiplication or Division Solve and graph each inequality. 8z < 32 –1 0 1 2 3 4 5 6 7 8 9 10 11 The empty circle at 4 shows that 4 is not a solution. Example 5 Graph the solution of the inequality on a number line. a >4 4 13 14 15 16 17 18 19 Example 6: Write an Inequality to Represent the Situation Six friends go to a restaurant. They have a gift certificate for $150. They plan to share it equally and spend no additional money. Write an inequality to describe how much each friend can spend. Example 7 Derek must log at least 20 hours of flight time for a sport pilot certificate. So far, he has logged 7 hours. Write and solve an inequality to describe how much more flight time Derek needs to log. Example 8: Solving Two-Step Inequalities Solve and graph each inequality. 3y + 6 > 12 –1 0 1 2 3 4 5 6 7 8 9 10 11 Example 9: Solving Two-Step Inequalities Solve and graph each inequality. t + 3 12 3 24 25 26 27 28 29 30 31 32 33 34 35 36 Example 10 Solve and graph each inequality. 2m-3<7 0 1 2 3 4 5 6 7 8 9 10 Example 11: Problem Solving Application The cost to rent a party room is $70. There is an additional fee of $8 per guest. How many guests can Jesse invite if he can spend no more than $150? Example 12 Hanley Ramirez plays baseball for the Florida Marlins. His batting average is his total hits divided by total at-bats, to the nearest thousandth. With two games remaining in the 2008 season, he had 173 hits and 581 atbats. If he gets 8 more at-bats, how many more hits must he get to have an average of at least .300?