To solve the equation \( \frac{2}{3}c - 2 = 2 + c \), follow these steps:
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Isolate the variable: Start by moving all terms involving \( c \) to one side of the equation and constant terms to the other side.
\[ \frac{2}{3}c - c = 2 + 2 \]
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Simplify the equation: Combine like terms. To subtract \( c \) from \( \frac{2}{3}c \), rewrite \( c \) as \( \frac{3}{3}c \):
\[ \frac{2}{3}c - \frac{3}{3}c = 4 \]
This simplifies to:
\[ -\frac{1}{3}c = 4 \]
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Solve for \( c \): To solve for \( c \), multiply both sides of the equation by \( -3 \):
\[ c = 4 \cdot (-3) \]
\[ c = -12 \]
The solution to the equation is:
\[ \boxed{-12} \]