To solve the equation \(-3 = \frac{5}{22}x + 7\), follow these steps:
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Isolate the term with \(x\) by subtracting 7 from both sides:
\[ -3 - 7 = \frac{5}{22}x \]
\[ -10 = \frac{5}{22}x \]
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Eliminate the fraction by multiplying both sides by \(\frac{22}{5}\):
\[ -10 \cdot \frac{22}{5} = x \]
Calculate the left side:
\[ x = \frac{-220}{5} \]
\[ x = -44 \]
Thus, the solution to the equation is:
\[ \boxed{-44} \]