1. Solving Multi-Step Inequalities
Lesson 6-3
Solving Multi-Step Inequalities

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4. Objectives Solve inequalities involving more than one operation
Solve linear inequalities involving the Distributive Property

5. Vocabulary
none

6. Multiplication and Division PoE
Properties of Equality (PoE) are based on the concept that as long as you do the same thing to both sides of an equation, then you have not changed anything.
Multiplication PoE
For any numbers a, b, and c, if a = b, then ac = bc
You can multiply both sides of an equation by the same thing without changing the equation
Division PoE
For any numbers a, b, and c with c ≠ 0, if a = b, then a/c = b/c
You can divide both sides of an equation by the same thing without changing the equation
Multiplication and division are reciprocal actions

7. Example 1 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.

8. Example 1 cont Original inequality Subtract 32 from each side.
Simplify.
Multiply each side by
Simplify.
Answer: Water will be a gas for all temperatures greater than 100°C.

9. Example 2 Solve 13 – 11d ≥ 79. Then check your solution.
Original inequality
Subtract 13 from each side.
Simplify.
Divide each side by –11 and change
Simplify.
Check To check the solution, substitute –6, a number less than –6, and a number greater than –6.
Answer: The solution set is

10. Example 3
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 number
plus
is less than
a number minus three.
twelve 4n +
< 12

11. Example 3 cont 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

12. Example 4 Original inequality Distributive Property
Combine like terms.
Add c to each side.
Simplify.
Subtract 6 from each side.
Simplify.
Divide each side by 4.
Simplify.
Answer: The solution set is

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

14. Summary & Homework Summary: Homework:
Multi-step inequalities can be solved by undoing the operations
Remember to reverse the inequality sign when multiplying or dividing each side by a negative number
When solving equations that contain grouping symbols, first use the Distributive Property to remove the grouping symbols
Homework:
Pg even