How do I solve absolute value equations and inequalities?

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Presentation transcript:

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

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 6 units l l l l l l l l l l l l l l l l l -4 -2 0 2 4 6 8 10

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

Solve Absolute Value Equations and Inequalities 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.

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

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

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

Solve Absolute Value Equations and Inequalities 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.

Solve Absolute Value Equations and Inequalities 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 l l l l l l l l l l l l l l l l -8 -6 -4 -2 0 2 4 6 8

Solve Absolute Value Equations and Inequalities 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 l l l l l l l l l l l l l l l l -8 -6 -4 -2 0 2 4 6 8

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

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

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

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

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

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