Find the Domain |3x-4|=x

Problem

|3*x−4|=x

Solution

1. Identify the nature of the equation. This is an absolute value equation where the expression inside the absolute value must be equal to the positive or negative value of the other side.

2. Apply the definition of absolute value to create two separate cases.

3. Set up the first case where the expression is positive: 3*x−4=x

4. Solve the first case by subtracting x from both sides and adding 4 to both sides.

3*x−x=4

2*x=4

x=2

5. Set up the second case where the expression is negative: 3*x−4=−x

6. Solve the second case by adding x to both sides and adding 4 to both sides.

3*x+x=4

4*x=4

x=1

7. Verify the solutions by substituting them back into the original equation to ensure the right side x is non-negative, as an absolute value cannot equal a negative number.

8. Check x=2 |3*(2)−4|=|2|=2 This is valid.

9. Check x=1 |3*(1)−4|=|−1|=1 This is valid.

Final Answer

x={1,2}

Want more problems? Check here!