10-4 Solving Inequalities Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

10-4 Solving Inequalities Warm Up Graph each number on the number line

10-4 Solving Inequalities 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 x = 20; Randy can play 10 games.

10-4 Solving Inequalities MA.6.A.3.2 Write, solve, and graph one- …step…inequalities. Sunshine State Standards

10-4 Solving Inequalities Vocabulary inequality solution of an inequality

10-4 Solving Inequalities 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 inequality is any value of the variable that makes the statement true.

10-4 Solving Inequalities Graph the solutions of each inequality on a number line. Additional Example 1: Graphing Inequalities A. t > 4 Draw an empty circle at 4 to show that 4 is not a solution. Draw an arrow to the right to show that values greater than 4 are solutions. B. y  Draw a solid circle at 11 to show that 11 is a solution. Draw an arrow to the left to show values that are equal to or less than 11 are also solutions.

10-4 Solving Inequalities Graph the solution of the inequality b ≤ 4 on a number line. Check It Out: Example

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

10-4 Solving Inequalities Solve and graph each inequality. Check It Out: Example < x < x or x > 2

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

10-4 Solving Inequalities Graph the solution of the inequality on a number line. Check It Out: Example a4a4 a4a4 a  16 > 4 4 ∙ > 4 ∙ 4

10-4 Solving Inequalities Additional Example 4: Write an Inequality to Represent the Situation Let m represent the amount the friends want to spend. 6 should be less than or equal to 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. times money need ≤ x m The inequality 6m ≤ 150 represents the situation.

10-4 Solving Inequalities 6m ≤ m ≤ 25 Each friend can spend up to $25. Divide both sides by 6 to undo the multiplication. Solve the inequality. 6m ≤ 150. Additional Example 4A Continued

10-4 Solving Inequalities Additional Example 4 Continued Check Substitute the input value into the rule. 6(25) ≤ 150 = 150 ≤ 150 check 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. 6(20) ≤ 150 = 120 ≤ 150 check

10-4 Solving Inequalities Check It Out: Example h > 20 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 > 13 Derek must log at least 13 more hours of flight time.