To solve the equation \( 2x - \frac{1}{3} = 7 \), follow these steps:
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First, eliminate the fraction by adding \(\frac{1}{3}\) to both sides of the equation:
\[ 2x - \frac{1}{3} + \frac{1}{3} = 7 + \frac{1}{3} \]
Simplifying this gives:
\[ 2x = 7 + \frac{1}{3} \]
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To add \(7\) and \(\frac{1}{3}\), convert \(7\) to a fraction with a common denominator:
\[ 7 = \frac{21}{3} \]
Now add:
\[ 2x = \frac{21}{3} + \frac{1}{3} = \frac{22}{3} \]
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Now, divide both sides by \(2\) to solve for \(x\):
\[ x = \frac{22}{3} \div 2 = \frac{22}{3} \cdot \frac{1}{2} = \frac{22}{6} = \frac{11}{3} \]
So, the solution is:
\[ x = \frac{11}{3} \]