To solve the equation \( 3x - \frac{4}{5} - 10 = -7 \), follow these steps:
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Combine like terms on the left side. \[ 3x - 10 - \frac{4}{5} = -7 \] To combine -10 and \(-\frac{4}{5}\), convert -10 to a fraction with a denominator of 5: \[ -10 = -\frac{50}{5} \] So, the equation becomes: \[ 3x - \frac{50}{5} - \frac{4}{5} = -7 \] Now combine the fractions: \[ 3x - \frac{54}{5} = -7 \]
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Isolate the term with \( x \) by adding \(\frac{54}{5}\) to both sides: \[ 3x = -7 + \frac{54}{5} \] Convert -7 to a fraction with a denominator of 5: \[ -7 = -\frac{35}{5} \] Now combine the fractions: \[ 3x = -\frac{35}{5} + \frac{54}{5} = \frac{54 - 35}{5} = \frac{19}{5} \]
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Divide both sides by 3 to solve for \( x \): \[ x = \frac{19}{5} \div 3 = \frac{19}{5} \times \frac{1}{3} = \frac{19}{15} \]
So the solution is: \[ x = \frac{19}{15} \]