To simplify the expression \( 3\left(\frac{2}{3}p + 3 - \frac{1}{3}p - 5\right) \), we first simplify the expression inside the parentheses:
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Combine the terms involving \( p \): \[ \frac{2}{3}p - \frac{1}{3}p = \left(\frac{2}{3} - \frac{1}{3}\right)p = \frac{1}{3}p \]
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Combine the constant terms: \[ 3 - 5 = -2 \]
So, we can rewrite the expression inside the parentheses: \[ \frac{1}{3}p - 2 \]
Now substituting this back into the expression: \[ 3\left(\frac{1}{3}p - 2\right) \]
Distributing the 3: \[ 3 \cdot \frac{1}{3}p - 3 \cdot 2 = p - 6 \]
Thus, the expression \( 3(2/3p + 3 - 1/3p - 5) \) simplifies to: \[ p - 6 \]
So, the equation that equals the given expression is: \[ p - 6 \]