Solve: `2/3 x+1=7/3`.

Options

A. `5`
B. `4`
C. `3`
D. `2`

Answer

To solve the equation \( \frac{2}{3}x + 1 = \frac{7}{3} \), we will follow these steps:

### Step 1: Isolate the term with \( x \)
We start with the equation:
\[ \frac{2}{3}x + 1 = \frac{7}{3} \]
To isolate the term with \( x \), we need to move \( 1 \) to the right side of the equation. We do this by subtracting \( 1 \) from both sides:
\[ \frac{2}{3}x = \frac{7}{3} - 1 \]

### Step 2: Convert \( 1 \) to a fraction with a common denominator
Next, we need to express \( 1 \) as a fraction with a denominator of \( 3 \):
\[ 1 = \frac{3}{3} \]
Now we can rewrite the equation:
\[ \frac{2}{3}x = \frac{7}{3} - \frac{3}{3} \]

### Step 3: Subtract the fractions
Now we perform the subtraction on the right side:
\[ \frac{2}{3}x = \frac{7 - 3}{3} = \frac{4}{3} \]

### Step 4: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by \( \frac{3}{2} \) (the reciprocal of \( \frac{2}{3} \)):
\[ x = \frac{4}{3} \cdot \frac{3}{2} \]

### Step 5: Simplify the right side
Now we simplify the right side:
\[ x = \frac{4 \cdot 3}{3 \cdot 2} = \frac{4}{2} = 2 \]

### Final Answer
Thus, the solution to the equation is:
\[ x = 2 \]

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