How do I solve absolute value equations and

• How do I solve absolute value equations and inequalities?

2. 2 Solve Absolute Value Equations and Inequalities Example 1 Solve a simple absolute value equation 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 l l -4 l l -2 l l 0 6 units l l 2 l l 4 l l 6 l l 8 l l 10 l

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

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

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 Example 3 Solve an inequality of the form 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 ____. l -8 l l -6 l l -4 l l -2 l l 0 l l 2 l l 4 l l 6 l l 8

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

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

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