To solve for \( x \) in the equation:
\[ 3 - \frac{6}{5}x = -3 \]
- Start by isolating the term with \( x \). Subtract 3 from both sides:
\[ -\frac{6}{5}x = -3 - 3 \]
This simplifies to:
\[ -\frac{6}{5}x = -6 \]
- Now, to get rid of the negative sign on the left side, multiply both sides by -1:
\[ \frac{6}{5}x = 6 \]
- Next, multiply both sides by the reciprocal of \( \frac{6}{5} \), which is \( \frac{5}{6} \):
\[ x = 6 \cdot \frac{5}{6} \]
- Simplifying this results in:
\[ x = 5 \]
Now let’s check the solution by substituting \( x = 5 \) back into the original equation:
Substituting \( x \):
\[ 3 - \frac{6}{5}(5) = 3 - 6 = -3 \]
Since both sides of the equation are equal, the solution is verified.
Thus, the final answer is:
\[ \boxed{5} \]
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