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.)