1. 4.1.1 – Solving Inequalities

2. All equations we have solved are considered problems of equality – Involves some kind of equal sign On the other hand, we could have inequalities which are problems not involving the use of equal signs

3. Types of Inequalities < = Less than ≤ = Less than or equal to > = Greater than ≥ = Greater than or equal to

4. Linear Inequalities A linear inequality is an inequality with a linear component (IE, think y = mx + b for linear) Solutions of the inequality are values that make the inequality true for the given variable

5. Solving Linear Inequalities Similarities to equations: – Will still use inverse operations – Isolate the variable of interest – Treat other letters or numbers as constants Differences: – Solutions will likely be many numbers – If multiply or divide by a negative number, must flip the sign

6. Example. Solve the inequality 2p > 12.

7. Example. Solve the inequality 4x + 5 ≤ 17

8. Flipping the Sign Example. Solve the inequality -5y + 2 > -13

9. Example. Solve the inequality 7 – 4x < 1 – 2x – Get variables to same side, first

10. Graphing Solutions on Number Line Once we solve the inequality, we may plot the solutions on a number line If x > a (or, whatever variable), open dot, then point arrow to the right If x < a (or, whatever variable), open dot, then point arrow to the left

11. If x ≥ a (or, whatever variable), closed dot, then point arrow to the right If x ≤ a (or, whatever variable), closed dot, then point arrow to the left

12. Example. Solve the inequality 4 – x < 5. Then plot your solution.

13. Example. Solve the inequality 2x – 3 ≥ x. Then plot your solution.

14. Assignment Pg. 175 4-9, 23-28, 29-32