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Agenda Tuesday, Dec. 1 Homework 11 p. 169 # 5 - 8, 10, 12, 16 - 18, 27 - 30, 40 - 44 correct homework Meet me in the computer lab tomorrow Absolute Value Equations & Inequalities Ch. 3 test on Thursday

Absolute Value Equations & Inequalities

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Page 1: Absolute Value Equations & Inequalities

Agenda Tuesday, Dec. 1

Homework 11 p. 169 # 5 - 8, 10, 12, 16 - 18, 27 - 30, 40 - 44

correct homework

Meet me in the computer lab tomorrow

Absolute Value Equations & Inequalities

Ch. 3 test on Thursday

Page 2: Absolute Value Equations & Inequalities
Page 3: Absolute Value Equations & Inequalities
Page 4: Absolute Value Equations & Inequalities
Page 5: Absolute Value Equations & Inequalities
Page 6: Absolute Value Equations & Inequalities

Absolute Value Equations

Absolute Value is the distance a number is from zero on a number line.

The absolute value of 4 would be at either -4 or +4.

If we write this as an equation, x = 4the two solutions of the equation x = -4 and +4

10 2 3 4 5 6 7 8 9 10-1-2

-3-4-5-6-7-8-9-10

Page 7: Absolute Value Equations & Inequalities

Solving Absolute Value Equations

x + 6 = 13- 6 - 6

x = 7

Using the definition of absolute value

x = 7 or x = -7

Check x + 6 = 13

7 + 6 = 13 or -7 + 6 = 13

7 + 6 = 13 or 7 + 6 = 13

Page 8: Absolute Value Equations & Inequalities
Page 9: Absolute Value Equations & Inequalities

Some absolute value equations have variable expressions within the absolute value symbol.

4n - 3 = 9Write two equations.

4n - 3 = 9 4n - 3 = -9 +3 +3 +3 +3

4n = 12 4n = -6n = 3 or n = -1 1/2

Page 10: Absolute Value Equations & Inequalities
Page 11: Absolute Value Equations & Inequalities

What is the solution?

3 n = -24

There is No solution - absolute value CANNOT be negative.

Page 12: Absolute Value Equations & Inequalities

Absolute Value Inequalities

x + 2 < 4 means the expression x + 2 is less than 4 spaces from zero on the number line

10 2 3 4 5 6 7 8 9 10-1-2

-3-4-5-6-7-8-9-10

x + 2 > 4 means the expression x + 2 is greater than 4 spaces from zero on the number line.

10 2 3 4 5 6 7 8 9 10-1-2

-3-4-5-6-7-8-9-10

Page 13: Absolute Value Equations & Inequalities

Solving Absolute Value Inequalities

Solve n - 5 < 3, graph the solution.

n - 5 < 3 and n - 5 > -3

+5 +5 +5 +5

n < 8 and n > 2

2 < n < 8

10 2 3 4 5 6 7 8 9 10-1-2

-3-4-5-6-7-8-9-10

Page 14: Absolute Value Equations & Inequalities

Solving Absolute Value Inequalities

Solve n - 5 > 3, graph the solution.

n - 5 > 3 OR n - 5 < -3

+5 +5 +5 +5

n > 8 OR n < 2

10 2 3 4 5 6 7 8 9 10-1-2

-3-4-5-6-7-8-9-10

Page 15: Absolute Value Equations & Inequalities
Page 16: Absolute Value Equations & Inequalities
Page 17: Absolute Value Equations & Inequalities

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