Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

Graph each number on the number line. Warm Up Graph each number on the number line. 1. 2 2. 7 3. 9 2 3 4 5 6 7 8 1 9 10

Problem of the Day Randy purchased a laser tag admission ticket for $5. Each time he plays, he pays an additional $1.50. Write an equation to find out how many games he can play if he has $20 to spend. 5 + 1.5x = 20; Randy can play 10 games.

Sunshine State Standards MA.6.A.3.2 Write, solve, and graph one- …step…inequalities.

Vocabulary inequality solution of an inequality

< > ≤ ≥ ≠ 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.

Additional Example 1: Graphing Inequalities Graph the solutions of each inequality on a number line. Draw an empty circle at 4to show that 4 is not a solution. Shade to the right to show that values greater than 4 are solutions. A. t > 1 2 3 4 5 6 7 8 B. y  11 Draw a solid circle at 11 to show that 11 is a solution. Shade to the left to show values that are equal to or less than 11are also solutions. 9 10 11 12 13 14 15

Graph the solution of the inequality b ≤ 4 on a number line. Check It Out: Example 1 Graph the solution of the inequality b ≤ 4 on a number line. 1 2 3 4 5 6 7 8 9 10

Solve and graph each inequality. Additional Example 2: Solving Inequalities with Addition or Subtraction Solve and graph each inequality. x – 3 ≥ 5 x – 3 ≥ 5 3 is subtracted from x. Add 3 to both sides of the inequality to undo the subtraction. + 3 + 3 x ≥ 8 5 6 7 8 9 10 11 4 3 2 1 – The solid circle at 8 shows that 8 is a solution.

Solve and graph each inequality. Check It Out: Example 2 Solve and graph each inequality. 5 < x + 3 7 6 5 4 3 2 1 5 < x + 3 -3 - 3 2 < x or x > 2

Solve and graph each inequality. Additional Example 3: Solving Inequalities with Multiplication or Division Solve and graph each inequality. 8z < 32 8z < 32 8 is multiplied by z. 8 8 Divide both sides of the inequality by 8 to undo the multiplication. z < 4 5 6 7 8 9 10 11 4 3 2 1 – The empty circle at 4 shows that 4 is not a solution.

Graph the solution of the inequality on a number line. Check It Out: Example 3 Graph the solution of the inequality on a number line. a 4 > 4 a 4 4 ∙ > 4 ∙ 4 a  16 13 14 15 16 17 18 19

Additional Example 4: 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. Let m represent the amount the friends want to spend. 6 times money need should be less than or equal to 150 6 x m ≤ 150 The inequality 6m ≤ 150 represents the situation.

Additional Example 4A Continued Solve the inequality. 6m ≤ 150. 6m ≤ 150 Divide both sides by 6 to undo the multiplication. 6 6 m ≤ 25 Each friend can spend up to $25.

Additional Example 4 Continued 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. Check Substitute the input value into the rule. 6(25) ≤ 150 = 150 ≤ 150 check 6(20) ≤ 150 = 120 ≤ 150 check

Derek must log at least 13 more hours of flight time. Check It Out: Example 4 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. 7 + h > 20 -7 -7 h > 13 Derek must log at least 13 more hours of flight time.

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 17 17

1. Graph the inequality x > 12 on the number line. Lesson Quiz 1. Graph the inequality x > 12 on the number line. Solve and graph each inequality. 2. 4 + x < 6 3.  11 12 13 14 15 16 17 x < 2 –3 –2 –1 0 1 2 3 y ≥ 32 32 33 34 35 36 37 38

Lesson Quiz for Student Response Systems 1. Identify the inequality. A. x < 1 B. x < 1 C. x > 1 D. x > 1 19 19

Lesson Quiz for Student Response Systems 2. Solve the inequality x + 3 < 9. A. x < 6 B. x < 12 C. x > 6 D. x > 12 20 20

Lesson Quiz for Student Response Systems 3. Solve the inequality . A. m < 5 B. m < 5 C. m > 36 D. m > 36 21 21