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

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: -.07 is less than 0 Test 2: 2 is not less than 0

[-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

(-∞,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

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

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