To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will follow the order of operations, apply the distributive property, and then combine like terms. Here are the steps:
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Distribute the 8 across the terms inside the parentheses \( (3x - 2) \): \[ 8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16 \]
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Substitute the distributed result back into the original expression: \[ 4 + (24x - 16) - 7x \]
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Combine like terms:
- First, combine the constant terms \( 4 \) and \( -16 \): \[ 4 - 16 = -12 \]
- Next, combine the \( x \) terms \( 24x \) and \( -7x \): \[ 24x - 7x = 17x \]
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Put it all together: \[ -12 + 17x \]
Thus, the simplified expression is: \[ \boxed{17x - 12} \]