%5E3%3D343.jpeg "(4x-1)^3=343")
Solving the Equation (4x-1)³ = 343
This article will guide you through solving the equation (4x-1)³ = 343. We will break down the steps to find the value of 'x'.
Step 1: Simplify the equation
The equation (4x-1)³ = 343 can be simplified by taking the cube root of both sides.
- Cube root of 343 is 7:
- This is because 7 * 7 * 7 = 343.
- Cube root of (4x-1)³ is (4x-1):
- The cube root cancels out the cube.
Therefore, the simplified equation is: (4x-1) = 7
Step 2: Solve for 'x'
Now, we have a simple linear equation: (4x - 1) = 7
- Add 1 to both sides:
- This gives us 4x = 8.
- Divide both sides by 4:
- This gives us x = 2.
Conclusion
Therefore, the solution to the equation (4x-1)³ = 343 is x = 2.
You can verify this answer by substituting 'x' back into the original equation:
- (4 * 2 - 1)³ = (8 - 1)³ = 7³ = 343.