1. Math Pacing Solving Multi-Step Inequalities Solve each inequality. 1.2. 3. Which inequality is not represented by the graph:

2. Solving Multi-Step Inequalities Solving inequalities involving more than one operation can be solved by undoing the operations in the same way you would solve an equation with more than one step.

3. Example 3-1a Science The inequality F > 212 represents the temperatures in degrees Fahrenheit for which water is a gas (steam). Similarly, the inequality represents the temperatures in degrees Celsius for which water is a gas. Find the temperature in degrees Celsius for which water is a gas. Solve a Real-World Problem

4. Example 3-1a Answer:Water will be a gas for all temperatures greater than 100°C. Original inequality Subtract 32 from each side. Simplify. Multiply each side by Simplify. Solve a Real-World Problem

5. Example 3-1b Science The boiling point of helium is –452°F. Solve the inequalityto find the temperatures in degrees Celsius for which helium is a gas. Answer:Helium will be a gas for all temperatures greater than –268.9°C. Solve a Real-World Problem Do this one in your notes, please! Subtract 32 from each side Multiply each side by 5/9

6. Example 3-2a Then check your solution. Original inequality Subtract 13 from each side. Simplify. Divide each side by –11 and change Simplify. Inequality Involving a Negative Coefficient

7. Example 3-2a Check To check the solution, substitute –6, a number less than –6, and a number greater than –6. Answer:The solution set is Inequality Involving a Negative Coefficient

8. Example 3-2b Then check your solution. Answer: Inequality Involving a Negative Coefficient Do this one in your notes, please! Subtract 3 from each side Divide each side by – 8 AND reverse the inequality

9. Example 3-3a Write an inequality for the sentence below. Then solve the inequality. Four times a number plus twelve is less than a number minus three. Four times a numberplus is less than a number minus three. twelve 4n4n+ < 12 Write and Solve an Inequality Let n = a number

10. Example 3-3a Original inequality Subtract n from each side. Simplify. Subtract 12 from each side. Simplify. Divide each side by 3. Simplify. Answer:The solution set is Write and Solve an Inequality

11. Example 3-3b Write an inequality for the sentence below. Then solve the inequality. 6 times a number is greater than 4 times the number minus 2. Answer: Write and Solve an Inequality

12. Solving Multi-Step Inequalities When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols.

13. Example 3-4a Original inequality Add c to each side. Simplify. Subtract 6 from each side. Simplify. Divide each side by 4. Simplify. Combine like terms. Distributive Property

14. Example 3-4a Answer: Sinceis the same as the solution set is Distributive Property

15. Example 3-4b Answer: Distributive Property Do this one in your notes, please! Subtract p from each side Distributive Property Combine like terms Add 2 to each side Divide each side by 3

16. Solving Multi-Step Inequalities If solving an inequality results in a statement that is always true, the solution is all real numbers. If solving an inequality results in a statement that is never true, the solution is the empty set . The empty set has no members.

17. Example 3-5a Answer:Since the inequality results in a false statement, the solution set is the empty set Ø. Original inequality Distributive Property Combine like terms. Subtract 4 s from each side. This statement is false. Empty Set

18. Example 3-5b Answer:Ø Empty Set Do this one in your notes, please! This statement is false. Distributive Property Combine like terms