1 College Algebra K/DC Wednesday, 03 December 2014 OBJECTIVE TSW solve and graph the solutions to linear inequalities, three-part inequalities, quadratic inequalities, and rational inequalities. ASSIGNMENT DUE –Sec. 1.6: p. 143 (7-12 all, odd, all, even)  wire basket

1-2 Inequalities 1.7 Linear Inequalities ▪ Three-Part Inequalities

1-3 Subtract 7. Divide by –2. Reverse the direction of the inequality symbol when multiplying or dividing by a negative number ! ! Solution set: Solving a Linear Inequality Havens’ Preference Use interval notation. Solve & graph:

1-4 Solving a Linear Inequality Subtract 8. Add 4x. Divide by 6. Solution set: Write the solution set in interval notation and graph it. Solve & graph:

1-5 Using Brackets vs. Parentheses With a strict inequality: Use parentheses. Ex:x > 4 ½ > x With an inequality that includes equals, use a bracket. Ex:x ≤ 9 x ≥ –1 “Infinity” and “Negative Infinity” ALWAYS get parentheses!!!

1-6 Interval Notation Always write the ends in numerical order. Ex:x < –9 (–∞, –9) not (–9, –∞) Ex:8 ≤ x[8, ∞) not (∞, 8] Make sure your brackets look like brackets and not squared- off parentheses! Make sure your parentheses look like parentheses and not rounded-off brackets! BOTTOM LINE: Write your answers neatly!

1-7 Solving a Three-Part Inequality Add 8 to all three parts. Divide by 6. Write the solution set in interval notation and graph it. Solution set: Solve & graph:

1-8 Assignment: Sec. 1.7: p. 155 (13-33 odd) Due before you go to lunch today (black tray). Solve each inequality. Write each solution set in interval notation and graph.

1-9 Inequalities 1.7 Quadratic Inequalities ▪ Rational Inequalities

1-10 Solving a Quadratic Inequality Solve. Step 1: Find the values of x that satisfy. or Step 2: The two numbers divide a number line into three regions. Use closed dots since the inequality symbol includes equality.

1-11 Solving a Quadratic Inequality Solve. Step 3: Choose any value in each of the intervals and find the sign of in each of the intervals. –46 0 +–+

1-12 Solving a Quadratic Inequality Solve. –46 0 +–+ Step 4: Since (negative), the solution is the interval that makes negative. Solution set: [–3, 5]

1-13 Solving Quadratic Inequalities Solve and graph each of the following: a) b)

1-14 Solving Rational Inequalities Solve and graph each of the following: d) e) f)

Assignment: Sec. 1.7: pp (39-44 all, all, odd, 78) Due on Wednesday, 10 December 2014 (TEST day). Solve each inequality. Write each solution in interval notation.