To simplify the expression \( 4(g - 2) + (g + 2) \), we can use the distributive property and combine like terms.
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Distribute \( 4 \) in \( 4(g - 2) \): \[ 4(g - 2) = 4g - 8 \]
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Now substitute this back into the original expression: \[ 4(g - 2) + (g + 2) = (4g - 8) + (g + 2) \]
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Combine like terms: \[ 4g + g - 8 + 2 = 5g - 6 \]
Thus, the simplified expression is: \[ \boxed{5g - 6} \]