Essential Questions

Wednesday, September 21 Essential Questions • How do I solve absolute value equations and inequalities?

2.2 Solve Absolute Value Equations and Inequalities l l l l l l l l l l l l l l l l l Solve a simple absolute value equation Example 1 Solve . Graph the solution. Write original equation. Write equivalent equations. Solve for x. Simplify. The solutions are ____ and ___. These are the values of x that are ___ units away from ___ on a number line. 6 units 6 units -4 -2 0 2 4 6 8 10

2.2 Solve Absolute Value Equations and Inequalities l l l l l l l l l l l l l l l l l l l l l l l l l l l l Checkpoint. Solve the equation. Then graph the solution 5 units 5 units -8 -6 -4 -2 0 2 4 6 8 2 units 2 units 0 1 2 3 4 5 6 7 8 9 10

2.2 Solve Absolute Value Equations and Inequalities Check for extraneous solutions Example 2 Solve . Check for extraneous solutions. Write original equation. Expressions can equal ____ or _____. Subtract _____ from each side. Solve for x. Check the apparent solutions to see if either is extraneous.

2.2 Solve Absolute Value Equations and Inequalities Check for extraneous solutions Example 2 Solve . Check for extraneous solutions. Check The solution is ___. Reject ____ because it is an ___________ solution. extraneous

2.2 Solve Absolute Value Equations and Inequalities Checkpoint. Solve the equation. Check for extraneous solutions.

2.2 Solve Absolute Value Equations and Inequalities Pg. 31 #1 and 17 Rewrite the absolute value equation as two linear equations. Solve the equation.

2.2 Solve Absolute Value Equations and Inequalities l l l l l l l l l l l l l l l l l Solve an inequality of the form . Example 3 Solve . Then graph the solution. The absolute value inequality is equivalent to First Inequality Second Inequality Write inequalities. Subtract __ from each side. Divide each side by ___. The solution are all real numbers less than ____ or greater than ____. -8 -6 -4 -2 0 2 4 6 8

2.2 Solve Absolute Value Equations and Inequalities l l l l l l l l l l l l l l l l l Solve an inequality of the form . Example 4 Solve . Then graph the solution. Write inequality. Write equivalent compound inequality. Add ____ to each expression. The solution is between ____ and ____, inclusive. -8 -6 -4 -2 0 2 4 6 8

2.2 Solve Absolute Value Equations and Inequalities l l l l l l l l l l l l l l l l l Checkpoint. Solve the inequality. Then graph the solution. -6 -4 -2 0 2 4 6 8 10

2.2 Solve Absolute Value Equations and Inequalities l l l l l l l l l Checkpoint. Solve the inequality. Then graph the solution. -3 -2 -1 0 1 2 3 4 5

2.2 Solve Absolute Value Equations and Inequalities Pg. 32 #21, 24, 36, and 37 Rewrite the absolute value inequality as a compound inequality.

2.2 Solve Absolute Value Equations and Inequalities Pg. 32 #21, 24, 36, and 37 Solve the inequality.

2.2 Solve Absolute Value Equations and Inequalities Pg. 31, 2.2 #1-43 Textbook pg 30 #1-15, 16-28

Essential Questions