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Warm-upDetermine the equation of this absolute value function.
Then, give the intervals of increase and decrease and the domain and range.
Math IIDay 40 (10-7-09)
UNIT QUESTION: How are absolute value equations similar to piecewise functions?Standard: MM2A1
Today’s Question:How do we solve absolute value inequalities?Standard: MM2A1.b,c
2.2 Solving Absolute Value 2.2 Solving Absolute Value Equations & InequalitiesEquations & Inequalities
p. 28-32
Absolute Value (of x)
• Symbol lxl
• The distance x is from 0 on the number line.
• Always positive
• Ex: l-3l=3
-4 -3 -2 -1 0 1 2
Ex: x = 5
• What are the possible values of x?
x = 5 or x = -5
PracticePractice
WorkbookWorkbookPage 31 #1-9Page 31 #1-9
To solve an absolute value equation:
ax+b = c, where c>0
(where c is positive)
To solve, set up 2 new equations, then solve each equation.
ax+b = c or ax+b = - c
** make sure the absolute value is by itself before you split to solve.
Ex: Solve 6x-3 = 15
6x-3 = 15 or 6x-3 = -15
6x = 18 or 6x = -12
x = 3 or x = -2
* Plug in answers to check your solutions!
Ex: Solve 2x + 7 -3 = 8
Get the abs. value part by itself first!
2x+7 = 11
Now split into 2 parts.
2x+7 = 11 or 2x+7 = -11
2x = 4 or 2x = -18
x = 2 or x = -9
Check the solutions.
Your Turn: Solve 2x - 5 = 9
To solve an absolute value inequality:
ax+b < c or ax+b ≤ c, where c>0
To solve, set up a compound “and” inequality with –c and c and solve.
Ex: Solve & graph.
• Becomes an “and” problem
2194 x
219421 x30412 x
2
153 x
-3 7 8
To solve an absolute value inequality:
ax+b > c or ax+b ≥ c, where c>0
To solve, set up a compound “or” inequality with -c and c and solve.
Solve & graph.
• Get absolute value by itself first.
• Becomes an “or” problem
11323 x
823 x
823or 823 xx63or 103 xx
2or 3
10 xx
-2 3 4
Your Turn: Solve & graph.
2 4 5 15x
PracticePractice
WorkbookWorkbookpage 32 #21, 23page 32 #21, 23
PracticePractice
WorkbookWorkbookpage 32 #22, 24-29page 32 #22, 24-29
Assignment
page 30 #7-25 (odd)page 30 #7-25 (odd)
