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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
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
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
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
What is the solution?
3 n = -24
There is No solution - absolute value CANNOT be negative.
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
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
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
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