To solve the equation \( 9x - (5x - 1) = 2 \), we will first simplify the left side of the equation.
-
Distribute the negative sign on the left side: \[ 9x - 5x + 1 = 2 \]
-
Combine like terms: \[ (9x - 5x) + 1 = 2 \] \[ 4x + 1 = 2 \]
-
Now, isolate the variable \( x \) by subtracting 1 from both sides: \[ 4x = 2 - 1 \] \[ 4x = 1 \]
-
Divide both sides by 4: \[ x = \frac{1}{4} \]
Now let's check the options provided:
- A. \(\frac{1}{14}\)
- B. \(\frac{1}{4}\)
- C. \(-\frac{1}{14}\)
- D. \(-\frac{1}{4}\)
The solution \( x = \frac{1}{4} \) corresponds to option B.
Thus, the final answer is: B. one fourth