To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will follow the order of operations, applying the distributive property, and combining like terms. Here’s how to do it step-by-step:
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Start with the original expression: \[ 4 + 8(3x - 2) - 7x \]
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Apply the distributive property to the term \( 8(3x - 2) \). Distributing \( 8 \) to both \( 3x \) and \(-2\): \[ 8 \cdot 3x + 8 \cdot (-2) = 24x - 16 \]
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Replace the distributed part back into the expression: \[ 4 + (24x - 16) - 7x \]
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Combine like terms. First, rearranging the expression helps to group the constants and the terms with \( x \): \[ (24x - 7x) + (4 - 16) \]
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Subtract the coefficients of \( x \): \[ 24x - 7x = 17x \]
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Subtract the constants: \[ 4 - 16 = -12 \]
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Combine both results: \[ 17x - 12 \]
So, the simplified expression is: \[ \boxed{17x - 12} \]