1. Calculus X Solving Inequalities Algebraically Unit 1
ES: Explicitly assess information and draw conclusions
Objective: Be able to solve inequalities algebraically.
Warm-Up: Factor the below expression

2. Solving quadratic inequalities
Steps:
1) Factor after setting to zero
2) Set each factor to zero then solve
3) Place on number line and test each region 1
4/3
Test 0: 4 is not less than 0
(1,4/3)
Test 1.1: is less than 0
Test 2: 2 is not less than 0

3. [-2,3] Steps: 1) Factor after setting to zero
2) Set each factor to zero then solve
3) Place on number line and test each region -2 3
Test -3: 6 is not less than 0
[-2,3]
Test 0: -6 is less than 0
Test 4: 6 is not less than 0

4. (-∞,2)U(4,∞) Steps: 1) Factor after setting to zero
2) Set each factor to zero then solve
3) Place on number line and test each region 2 4
Test 0: 8 is greater than 0
(-∞,2)U(4,∞)
Test 3: -1 is not greater than 0
Test 5: 3 is greater than 0

5. Solving rational inequalities
Steps:
1) Make sure fraction is set to zero
2) Set num & denom to zero then solve. Notice the denom can’t be zero, so it will get an open circle no matter what!
3) Place on number line and test each region -2 3
*Can’t divide by 0 so can’t include 3
Test -3: 1/6 is not less than 0
Test 0: -2/3 is less than 0
[-2,3)
Test 4: 6 is not less than 0

6. Can’t factor and no variables in the denominator, so nothing fancy.
(-∞,12/7]