1. Objective: Section 1.6 Solving Linear Inequalities 1 5 Minute Check  Solve the following equations. 1. 7x – 4 = 5x + 2 2. 10 – 3y = 16y – 9 3.

2. 2 1. How to solve simple inequalities (and graph them on a number line). 2. You will also learn how to solve compound inequalities. Investigation: 1. Write two true inequalities involving integers using. Example -6 < 3 2. Add, subtract, multiply and divide each side of your inequality by 2 and -2. In each case, decide whether the new inequality is true or false. 3. What can you conclude? What will you learn today?

3. Objective: Section 1.6 Solving Linear Inequalities 3 Linear Inequalities Inequalities such as x 9 are examples of linear inequalities in a single variable. A solution of an inequality in one variable is a value of the variable that makes the inequality true. What are some of the solutions to x < 9?

4. Objective: Section 1.6 Solving Linear Inequalities 4 Graphing Inequalities The graph of an inequality in one variable consists of all points on a real number line that correspond to solutions of the inequality. Graph x > 3. When do you use an open dot or a closed dot? How would you graph -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

5. Objective: Section 1.6 Solving Linear Inequalities 5 1. Solving an Inequality with a Variable on One Side Example: Solve 5y – 8 < 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

6. Objective: Section 1.6 Solving Linear Inequalities 6 You Try  Solve 11y – 9 > 13 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

7. Objective: Section 1.6 Solving Linear Inequalities 7 2. Solving an Inequality with Variables on Both Sides  Solve 2x + 1 < 6x – 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

8. Objective: Section 1.6 Solving Linear Inequalities 8 You Try  Solve 7x + 9 > 10x – 12 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

9. Objective: Section 1.6 Solving Linear Inequalities 9 A Real-World Example  The weight w (in pounds) of an Icelandic saithe is given by W = 10.4t – 2.2 Where t is the age of the fish in years. Describe the ages of a group of Icelandic saithe that weight up to 29 pounds.

10. Objective: Section 1.6 Solving Linear Inequalities 10 Solving Compound Inequalities A compound inequality is two simple inequalities joined by “and” or “or”. Example: -2 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

11. Objective: Section 1.6 Solving Linear Inequalities 11 Solving an “And” Compound Inequality  Solve: -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

12. Objective: Section 1.6 Solving Linear Inequalities 12 You Try  Solve -12 < 3x – 3 < 15 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

13. Objective: Section 1.6 Solving Linear Inequalities 13 You Try  Solve -2x + 7 < 3 or 3x + 5 < 2 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

14. Objective: Section 1.6 Solving Linear Inequalities 14 4. Solving an “Or” Compound Inequality  Solve:2x + 3 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9

15. Objective: Section 1.6 Solving Linear Inequalities 15 Homework Page 45, 13-18 all, 20, 28, 30, 38, 44, 50