To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations and utilize the distributive property. Here's a step-by-step breakdown of the simplification process:
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Distributive Property: First, we need to apply the distributive property to the term \( 8(3x - 2) \): \[ 8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16 \]
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Substituting Back into the Expression: Now we can substitute \( 24x - 16 \) back into the original expression: \[ 4 + (24x - 16) - 7x \]
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Combining Like Terms: Next, combine the constant terms and the variable terms:
- First, combine the constants: \( 4 - 16 = -12 \)
- Then combine the \( x \) terms: \( 24x - 7x = 17x \)
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Final Expression: Putting it all together, we get: \[ 17x - 12 \]
So, the simplified expression is: \[ \boxed{17x - 12} \]