To find the value of \( b \) that makes the expressions \((16k + 14) - (13k - 2) - (8k + 4)\) and \( bk + 8 \) equivalent, we first need to simplify the first expression.
Start with the expression: \[ (16k + 14) - (13k - 2) - (8k + 4) \]
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Distribute the negative sign through the parentheses: \[ = 16k + 14 - 13k + 2 - 8k - 4 \]
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Combine like terms:
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Combine the \( k \) terms: \[ 16k - 13k - 8k = (16 - 13 - 8)k = -5k \]
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Combine the constant terms: \[ 14 + 2 - 4 = 12 \]
Putting it all together, we have: \[ (16k + 14) - (13k - 2) - (8k + 4) = -5k + 12 \]
Now we equate this expression to \( bk + 8 \): \[ -5k + 12 = bk + 8 \]
Next, we compare coefficients of \( k \) and the constant terms on both sides:
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For the coefficients of \( k \): \[ -5 = b \]
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For the constant terms: \[ 12 = 8 \] This condition is automatically satisfied after we balance the variable coefficients.
Thus, the value of \( b \) is: \[ \boxed{-5} \]