Section+2.8

= 2.8 Solving Inequalities = __Polynomial Inequalities:__ Steps: 1. Get a zero on one side of the inequality 2. Find the values that make the equation equal 0 3. Place these values on a number line and test each interval 4. Shade the intervals which satisfy the inequality

2x^3-7x^2-10x+24>0 2x^3-7x^2-10x+24=0
 * Ex.**

Use calculator

__-2 I__ 2 -7 -10 24 __-4 22 -24__ 2 -11 12 0

2x^2-11x+12=0 (2x-3)(x-4)=0 x=3/2,4,-2

Show graphically-

Test:-3, 0, 2, 5 to tell if it is True or False <--F--o//**--T--**//o--F--o**//--T--//>** -2, 3/2, 4 (suppose to be under o's)

Answer: (-2,3/2)U(4,+infinity)

__Rational Inequalities:__ Steps: Same steps as polynomials except we include the values that make the denominator equal zero on the number line

((5)/(x+3))+((3)/(x-1))<0 (x+3)(x-1)(((5)/(x+3))+((3)/(x-1)))=(0)(x+3)(x-1) 5(x-1)+3(x+3)=0 5x-5+3x+9=0 8x+4=0 8x=-4 x=1/2
 * Ex.**

Asymptotes: x+3=0 x-1=0
 * x=-3**
 * x=1**

Show graphically-

Test: -4, -1, 0, 2 to tell us if it is True or False //**<--T--**//o--F--o//**--T--**//o--F--> -3,-1/2,1 (suppose to be under o's)

Answer: (-infinity,-3)U(-1/2,1)

__**Homework for the section:**__ Monday, 17- Page 265 #33-53 odd Tuesday, 18 (review for quiz tomarrow)- Page 270 #75-82