To solve the equation \(3x - \frac{4}{5} = -\frac{1}{2}\), follow these steps:
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First, add \(\frac{4}{5}\) to both sides of the equation to isolate the term with \(x\):
\[ 3x = -\frac{1}{2} + \frac{4}{5} \]
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To add the fractions on the right-hand side, find a common denominator. The least common multiple of 2 and 5 is 10.
Convert \(-\frac{1}{2}\) and \(\frac{4}{5}\) to have a denominator of 10:
\[ -\frac{1}{2} = -\frac{5}{10} \] \[ \frac{4}{5} = \frac{8}{10} \]
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Now substitute these back into the equation:
\[ 3x = -\frac{5}{10} + \frac{8}{10} \]
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Combine the fractions:
\[ 3x = \frac{3}{10} \]
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Finally, divide both sides by 3 to solve for \(x\):
\[ x = \frac{3}{10} \div 3 = \frac{3}{10} \cdot \frac{1}{3} = \frac{3}{30} = \frac{1}{10} \]
Thus, the value of \(x\) is:
\[ \boxed{\frac{1}{10}} \]
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