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1 4 solving absolute value equations2
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only

1 4 solving absolute value equations3
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only

1 4 solving absolute value equations4
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

1 4 solving absolute value equations5
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5|

1 4 solving absolute value equations6
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5

1 4 solving absolute value equations7
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| =

1 4 solving absolute value equations8
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

1 4 solving absolute value equations9
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1 4 solving absolute value equations10
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=

1 4 solving absolute value equations11
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4

1 4 solving absolute value equations12
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 +

1 4 solving absolute value equations13
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5

1 4 solving absolute value equations14
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3)

1 4 solving absolute value equations15
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

1 4 solving absolute value equations16
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4

1 4 solving absolute value equations17
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 +

1 4 solving absolute value equations18
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15

1 4 solving absolute value equations19
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

1 4 solving absolute value equations20
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

=1.4

1 4 solving absolute value equations21
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

=1.4 +

1 4 solving absolute value equations22
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

=1.4 + |-22|

1 4 solving absolute value equations23
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

=1.4 + |-22|

=1.4

1 4 solving absolute value equations24
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

=1.4 + |-22|

=1.4 +

1 4 solving absolute value equations25
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

=1.4 + |-22|

=1.4 + 22

1 4 solving absolute value equations26
1.4 – Solving Absolute Value Equations

Absolute Value–unit value only (w/o signs)

ex. |-5| = 5; |5| = 5

Example 1

Evaluate 1.4+|5y – 7| if y=-3

1.4+|5y – 7|=1.4 + |5(-3) – 7|

=1.4 + |-15 – 7|

=1.4 + |-22|

=1.4 + 22

= 23.4

slide32
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5

slide33
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5

slide34
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5

slide35
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

slide36
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

slide37
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18

slide38
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18

x = 23

slide39
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23

slide40
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

slide41
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3

slide42
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

slide43
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

slide44
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

slide45
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

slide46
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note:

slide47
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note: Absolute value cannot equal a negative number!

slide48
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note: Absolute value cannot equal a negative number!

slide49
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note: Absolute value cannot equal a negative number!

slide50
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note: Absolute value cannot equal a negative number!

slide51
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note: Absolute value cannot equal a negative number!

slide52
Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5 x – 18 = -5

+18 +18 +18 +18

x = 23 x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note: Absolute value cannot equal a negative number!

x = Ø

slide57
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2

slide58
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2

slide59
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

slide60
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

slide61
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6

slide62
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 =

slide63
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x

slide64
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x –

slide65
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

slide66
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2

slide67
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6

slide68
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x

slide69
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

slide70
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x

slide71
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x

-2x + 6 = -2

slide72
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x

-2x + 6 = -2

- 6 -6

slide73
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x

-2x + 6 = -2

- 6 -6

-2x

slide74
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x

-2x + 6 = -2

- 6 -6

-2x = -8

slide75
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x

-2x + 6 = -2

- 6 -6

-2x = -8

-2 -2

slide76
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x

-2x + 6 = -2

- 6 -6

-2x = -8

-2 -2

x = 4

slide77
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2

- 6 -6

-2x = -8

-2 -2

x = 4

slide78
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x

- 6 -6

-2x = -8

-2 -2

x = 4

slide79
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6

- 6 -6

-2x = -8

-2 -2

x = 4

slide80
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6

-2x = -8

-2 -2

x = 4

slide81
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -8

-2 -2

x = 4

slide82
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -8 4x = -4

-2 -2

x = 4

slide83
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4

slide84
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1

slide85
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1

slide86
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1

slide87
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1

slide88
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1

slide89
Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)

x + 6 = 3x – 2 x + 6 = -3x + 2

-3x -3x+3x +3x

-2x + 6 = -2 4x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1

ad