1. 2.8 - Solving Equations in One Variable

2. By the end of today you should be able to……. Solve Rational Equations Eliminate Extraneous solutions Solve Polynomial Inequalities Solve Rational & other Inequalities

3. Solving Rational Equations Rational Equations: equations involving rational expressions or fractions and can be written in the form of: f(x) g(x) where f(x) and g(x) are polynomial functions with no common factors and the zeros of f(x) are the solutions of the equations. Extraneous Solutions: Not solutions of the original equations. = 0

4. You Try! Solve the equation algebraically. Check for extraneous solutions. Support your answers numerically x + 2 = 15 x Solve Algebraically: Support Numerically:

5. x + 4x = 12 x - 3 x - 3 Solve the equation algebraically. Check for extraneous solutions. Support your answers numerically Solve Algebraically: Check Numerically:

6. Solve the equation graphically. Confirm your answer algebraically and identify extraneous solutions 2- 1 = 1 x + 1 x 2 + x Solve Graphically:Check Algebraically:

7. Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. x – 3 - 3 + 3 = 0 x x + 1 x 2 + x Check Graphically:Solve Algebraically:

8. 2.9 – Solving Inequalities in One Variable

9. Polynomial Inequalities To solve the inequality f(x) > 0 is to find the values of x that make f(x) positive x + 5 > 0 To solve the inequality f(x) < 0 is to find values of x that make f(x) negative x + 5 < 0

10. Where is the polynomial zero, positive, or negative? f(x) = (x + 2)(x + 1)(x – 5) a)x values that cause f(x) to be zero? a)x values that cause f(x) to be positive? a)x values that cause f(x) to be negative?

11. Solve the polynomial inequality graphically: x 3 – x 2 – 2x ≥ 0 Solve graphically: Check:

12. Solve the inequality: x 3 (x – 2) (x + 3) 2 < 0

13. You Try! Complete the factoring if needed, and solve the polynomial inequality using a sign chart. (x + 1)(x - 3) 2 > 0

14. You Try! Solve the equation graphically. Confirm your answer algebraically and identify extraneous solutions x + 6 = -7 x

15. You Try! Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically. 4x + 3 = 15 x + 4 x – 1 x 2 + 3x -4

16. Don’t Forget your Homework! Pg. 254-256 (#4-32 every 4) Pg. 265 – 266 (#4-50 every 4)