Solve for x.
(l is the absoulte bar, not one)
3*l 3x-2 l -6 > l 3x-2 l
We're given;
3*|3x-2|-6 >|3x-2|
Add -|3x-2| to both sides to get
2*|3x-2|-6 >0
Add 6 to both sides to get
2*|3x-2|>6
Divide both sides by 2
|3x-2|>3
This means 3x-2>3 or 3x-2<-3
3x-2>3 means 3x > 5 or x > 5/3
3x-2<-3 means 3x < -1 or x < -1/3
Be sure to test some values to verify this.
To solve for x, we follow these steps:
1. Start with the equation: 3*|3x-2|-6 > |3x-2|
2. Add -|3x-2| to both sides: 2*|3x-2|-6 > 0
3. Add 6 to both sides: 2*|3x-2| > 6
4. Divide both sides by 2: |3x-2| > 3
5. Now, we have two cases to consider:
a) 3x-2 > 3
b) 3x-2 < -3
For case a):
6. Solve for x: 3x-2 > 3
a) Add 2 to both sides: 3x > 5
b) Divide both sides by 3: x > 5/3
Therefore, x is greater than 5/3.
For case b):
7. Solve for x: 3x-2 < -3
a) Add 2 to both sides: 3x < -1
b) Divide both sides by 3: x < -1/3
Therefore, x is less than -1/3.
To verify the solutions, you can substitute test values for x into the original inequality. For example, if we choose a value greater than 5/3, like x = 2, we get:
3*|3(2)-2|-6 > |3(2)-2|
3*|6-2|-6 > |6-2|
3*4-6 > 4
6 > 4
Since the inequality holds true, we can conclude that x > 5/3 satisfies the inequality. Similarly, you can verify x < -1/3.