# 1.4 – Solving Absolute Value Equations. Absolute Value.

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1.4 – Solving Absolute Value Equations

Absolute Value

1.4 – Solving Absolute Value Equations Absolute Value–unit value only

1.4 – Solving Absolute Value Equations Absolute Value–unit value only

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

1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5|

1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5

1.4 – Solving Absolute Value Equations Absolute Value–unit value only (w/o signs) ex. |-5| = 5; |5| =

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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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

Example 2

Example 2 Solve |x – 18| = 5.

|x – 18| = 5

Example 2 Solve |x – 18| = 5. |x – 18| = 5

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 x = 23

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13

Example 2 Solve |x – 18| = 5. |x – 18| = 5 x – 18 = 5x – 18 = -5 +18 +18 +18 +18 x = 23x = 13 Example 3

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.

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

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

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 |5x – 6| = -9

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 |5x – 6| = -9 Note:

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 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

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 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

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 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

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 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

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 |5x – 6| = -9 Note: Absolute value cannot equal a negative number!

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 |5x – 6| = -9 Note: Absolute value cannot equal a negative number! x = Ø

Example 4

Example 4 Solve |x + 6| = 3x – 2.

|x + 6| = 3x – 2

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

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

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

Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2)

Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2)

Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6

Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 =

Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x

Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x –

Example 4 Solve |x + 6| = 3x – 2. |x + 6| = 3x – 2 x + 6 = 3x – 2 x + 6 = -(3x – 2) x + 6 = -3x – (-2)

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

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

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

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

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

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 -2x + 6 = -2

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

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

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 -2x + 6 = -2 - 6 -6 -2x = -8

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 -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2

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 -2x + 6 = -2 - 6 -6 -2x = -8 -2 -2 x = 4

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

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

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

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

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

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

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

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

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

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

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

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

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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