1. 2.1 – 2.2 Solving Linear Inequalities
EQ: How can you use an inequality to describe a real-life statement?

2. rather than ONE set number
What’s an inequality?
Is a range of values,
rather than ONE set number
An algebraic relation showing that a quantity is greater than or less than another quantity.
Speed limit:

3. Symbols Less than Greater than Less than OR EQUAL TO
Greater than OR EQUAL TO

4. Solving an Inequality x < 8 Solve using addition:
Solving a linear inequality in one variable is much like solving a linear equation in one variable. Get the variable to one side using the opposite operations.
Solve using addition:
x – 3 < 5
Add the same number to EACH side.
x < 8

5. Solving Using Subtraction
Subtract the same number from EACH side.

6. Using Subtraction…
Graph the solution.

7. Using Addition…

8. THE TRAP…..
When you multiply or divide each side of an inequality by a negative number, you must FLIP the inequality sign to maintain a true statement.

9. Solving using Multiplication
Multiply each side by the same positive number.
(2)

10. Solving Using Division
Divide each side by the same positive number. 3

11. Solving by multiplication of a negative #
Multiply each side by the same negative number and REVERSE the inequality symbol.
Multiply by (-1).
(-1)
See the switch

12. Solving by dividing by a negative #
Divide each side by the same negative number and reverse the inequality symbol. -2