Solve `3x + 2/3 = 2x + 1`

Options

A. `1/4`
B. `1/3`
C. `1/5`
D. `1/7`

Answer

To solve the equation \(3x + \frac{2}{3} = 2x + 1\), we will follow these steps:

### Step 1: Move all terms involving \(x\) to one side and constant terms to the other side.
We can do this by subtracting \(2x\) from both sides and subtracting \(\frac{2}{3}\) from both sides.

\[ 3x - 2x = 1 - \frac{2}{3} \]

### Step 2: Simplify the left side.
On the left side, we have:

\[ 3x - 2x = 1x = x \]

So, the equation now looks like:

\[ x = 1 - \frac{2}{3} \]

### Step 3: Simplify the right side.
To simplify \(1 - \frac{2}{3}\), we need a common denominator. The common denominator for 1 (which can be written as \(\frac{3}{3}\)) and \(\frac{2}{3}\) is 3.

\[ 1 = \frac{3}{3} \]

Now we can perform the subtraction:

\[ x = \frac{3}{3} - \frac{2}{3} = \frac{3 - 2}{3} = \frac{1}{3} \]

### Step 4: Write the final answer.
Thus, the solution to the equation \(3x + \frac{2}{3} = 2x + 1\) is:

\[ x = \frac{1}{3} \]

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