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1.4 – Solving Absolute Value Equations

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1 4 solving absolute value equations

1.4 – Solving Absolute Value Equations


1 4 solving absolute value equations1

1.4 – Solving Absolute Value Equations

Absolute Value


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


1 4 solving absolute value equations

Example 2


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18

x = 23


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 13


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 13

Example 3


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 13

Example 3 Solve |5x – 6| + 9 = 0.


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 13

Example 3 Solve |5x – 6| + 9 = 0.

|5x – 6| + 9 = 0

-9 -9

|5x – 6| = -9

Note:


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 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!


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 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!


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 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!


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 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!


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 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!


1 4 solving absolute value equations

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

x – 18 = 5x – 18 = -5

+18 +18 +18 +18

x = 23x = 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


1 4 solving absolute value equations

Example 4


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 =


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x –


1 4 solving absolute value equations

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

x + 6 = 3x – 2 x + 6 = -(3x – 2)

x + 6 = -3x – (-2)


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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


1 4 solving absolute value equations

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 = -24x

- 6 -6

-2x = -8

-2 -2

x = 4


1 4 solving absolute value equations

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 = -24x + 6

- 6 -6

-2x = -8

-2 -2

x = 4


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6

-2x = -8

-2 -2

x = 4


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -8

-2 -2

x = 4


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2

x = 4


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1


1 4 solving absolute value equations

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 = -24x + 6 = 2

- 6 -6 - 6 -6

-2x = -84x = -4

-2 -2 4 4

x = 4 OR x = -1


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