To solve the equation \( 2 - \frac{6}{5}x = -3 \), we can follow these steps:
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Isolate the term with \( x \): \[ -\frac{6}{5}x = -3 - 2 \] This simplifies to: \[ -\frac{6}{5}x = -5 \]
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Multiply both sides by -1 to eliminate the negative sign: \[ \frac{6}{5}x = 5 \]
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Multiply both sides by the reciprocal of \(\frac{6}{5}\), which is \(\frac{5}{6}\): \[ x = 5 \cdot \frac{5}{6} \] This simplifies to: \[ x = \frac{25}{6} \]
Thus, the solution is: \[ x = \frac{25}{6} \]