To simplify the expression \( 4b + 3c - 2b + 7c \), we start by combining the like terms.
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Combine the \( b \) terms: \[ 4b - 2b = 2b \]
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Combine the \( c \) terms: \[ 3c + 7c = 10c \]
Putting it all together, we have: \[ 2b + 10c \]
Thus, the simplified expression is \( 2b + 10c \).
The correct answer is: 2b + 10c
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