1.4 – solving absolute value equations. absolute value
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1.4 – Solving Absolute Value Equations
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=-31.4+|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=-31.4+|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=-31.4+|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=-31.4+|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=-31.4+|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=-31.4+|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=-31.4+|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=-31.4+|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.
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 = 5 x – 18 = -5
Example 2 Solve |x – 18| = 5.
|x – 18| = 5
x – 18 = 5 x – 18 = -5
Example 2 Solve |x – 18| = 5.
|x – 18| = 5
x – 18 = 5 x – 18 = -5
+18 +18
Example 2 Solve |x – 18| = 5.
|x – 18| = 5
x – 18 = 5 x – 18 = -5
+18 +18
x = 23
Example 2 Solve |x – 18| = 5.
|x – 18| = 5
x – 18 = 5 x – 18 = -5
+18 +18 +18 +18
x = 23
Example 2 Solve |x – 18| = 5.
|x – 18| = 5
x – 18 = 5 x – 18 = -5
+18 +18 +18 +18
x = 23 x = 13
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
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.
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
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
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
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:
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!
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!
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!
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!
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!
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
Example 4
Example 4 Solve |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
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 -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 -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 -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 -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 -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 -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 -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 = -2 4x
- 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 4x + 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 = -2 4x + 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 4x + 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 = -2 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -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 = -2 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -4 -2 -2 4 4x = 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 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -4 -2 -2 4 4x = 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 = -2 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -4 -2 -2 4 4x = 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 = -2 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -4 -2 -2 4 4x = 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 = -2 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -4 -2 -2 4 4x = 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 = -2 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -4 -2 -2 4 4x = 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 = -2 4x + 6 = 2
- 6 -6 - 6 -6-2x = -8 4x = -4 -2 -2 4 4x = 4 OR x = -1