Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities...

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Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify results. a) Solve using tables, graphs, and algebraic properties.

Transcript of Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities...

Page 1: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Section 1-5: Absolute Value Equations and Inequalities

Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify

results. a) Solve using tables, graphs, and algebraic properties.

Page 2: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Essential Question

How do I solve absolute value equations and inequalities?

Page 3: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Solving Absolute Value Equations

• Treat absolute value bars as grouping symbols• Follow order of operations• Definition of absolute value– If then – If then

0x xx

0x xx

Page 4: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Examples

• Solve for y

• Solve for x

15342 y

723 x

Page 5: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Extraneous Solution

• An extraneous solution is a solution of an equation derived from an original equation, that is NOT a solution of the original equation.

• Example. 932 x

Page 6: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Absolute Value Inequalities

• Let k represent a positive real number…

• is equivalent to or • *Greator

• is equivalent to and • Less Thand

kx kx kx

kx kx kx

Page 7: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Examples

• Solve for x

• Solve for x

1263 x

159623 x

Page 8: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Classwork

• P. 37 #34-66 All

Page 9: Section 1-5: Absolute Value Equations and Inequalities Goal 2.08: Use equations and inequalities with absolute value to model and solve problems; justify.

Homework

• P. 38 Section 1-5 #73-83


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