Solve absolute value equations in 1 and 2 var.
Solve absolute value inequalities in 1 and 2 var
The learner will
Solving Inequalities Reminder
Add this to the left “aha” column of your notes
We will use this rule in todays lesson
trick < ….. Is less than….think….is less thAND>……is greater than….think…..is greatOR
Solve Absolute Value Inequalities (1 var.)
Add this to the left “aha” column of your notes
How to solve an absolute value equation (1 var.)
52 x If = 6….then x could be either ______ or _______x -66
How to solve an absolute value equation (1 var.)
52 x If = 6….then x could be either ______ or _______x
+2 +2 -2 -2
X = {-3 , 7}
x – 2 = 5 or -x + 2 = 5
-66
x = 7 or -x = 3
Solve/Graph Absolute Value Equations
12332 x 75545 x
633633 xorx
9333 xorx
31 xorx
15541554 xorx
104204 xorx
2
55
xorx
1554 x
}3,1{x }5,2
5{x
633 x
Solve Absolute Value Inequality (1 Var)
|-2x +7| + 5 ≥ 14
x ≤ -1 OR x ≥ 8
- 5 - 5
|-2x +7| ≥ 9
-2x + 7 ≥ 9 or 2x - 7 ≥ 9- 7 - 7 + 7 +7
-2x ≥ 2 or 2x ≥ 16- 2 - 2 2 2
-1 8
Solve/Graph Absolute Value Inequalities
752 x 523
1x
752752 xandx
22122 xandx
16 xandx
523
152
3
1 xorx
33
17
3
1 xorx
921 xorx
-1 6
21-9
2
1
Now...2 variables…
We will not use shifting(translating) the
parent function today – it will be shown soon!
42 xy
2 Equations:
y = x + 2 - 4y = x - 2
y = -x - 2 - 4
y = -x - 6
Enter the absolute value equation in the TI84 to see the graph
Discuss: My 2 equations produce 2 lines, but the graph looks like a “V”….how could the 2 lines make that graph?
Absolute Value Equation (2 Var.)
Equation: 42 xy
Vertex: (-2,-4)Equations:
y=x-2y=-x-6
-2-2
-x-6x-2
Graph changes from a negative slope to a positive slope at x = – 2
21 xy
y= y=2)1( x
3 xy
2)1( x
1xy
13 x
33 x 1
1
Graph changes slope at x=1
Absolute Value Inequality (2 Var.)