What is the solution to the equation 9x-(3x-1)=3 ?

Options

A. `-3`
B. `-2/3`
C. `1/3`
D. `2/3`

Answer

To solve the equation \( 9x - (3x - 1) = 3 \), we will follow these steps:

### Step 1: Simplify the equation
Start by distributing the negative sign across the terms inside the parentheses:
\[ 9x - (3x - 1) = 9x - 3x + 1 \]
This simplifies to:
\[ 9x - 3x + 1 = 3 \]

### Step 2: Combine like terms
Now, combine the like terms on the left side:
\[ (9x - 3x) + 1 = 3 \]
This simplifies to:
\[ 6x + 1 = 3 \]

### Step 3: Isolate the variable
Next, we need to isolate \( x \). Start by moving the constant term (1) to the right side of the equation:
\[ 6x = 3 - 1 \]
This simplifies to:
\[ 6x = 2 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 6 to solve for \( x \):
\[ x = \frac{2}{6} \]
This can be simplified to:
\[ x = \frac{1}{3} \]

### Final Answer
Thus, the solution to the equation is:
\[ x = \frac{1}{3} \]

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