To simplify the expression \(4 + 8(3x - 2) - 7x\), we will apply the order of operations and the distributive property step by step.
Step 1: Distribute the \(8\)
We need to distribute \(8\) to both terms inside the parentheses \(3x - 2\):
\[ 8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16 \]
Step 2: Substitute back into the expression
Now we substitute \(24x - 16\) back into the original expression:
\[ 4 + (24x - 16) - 7x \]
Step 3: Combine like terms
Next, we will rearrange and combine all the terms. First, we can rewrite the expression:
\[ = 4 - 16 + 24x - 7x \]
Now, combine the constants \(4\) and \(-16\):
\[ 4 - 16 = -12 \]
Then, combine the \(x\) terms \(24x - 7x\):
\[ 24x - 7x = 17x \]
Step 4: Write the final simplified expression
Putting it all together, we have:
\[ -12 + 17x \]
Thus, the expression \(4 + 8(3x - 2) - 7x\) simplifies to:
\[ \boxed{17x - 12} \]
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