To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations, using the distributive property where necessary. Let's break it down step by step.
Step 1: Distribute the \( 8 \) into \( (3x - 2) \)
\[ 8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16 \]
Step 2: Substitute back into the expression
Now we substitute \( 24x - 16 \) back into the expression: \[ 4 + (24x - 16) - 7x \]
Step 3: Remove the parentheses
This can be simplified to: \[ 4 + 24x - 16 - 7x \]
Step 4: Combine like terms
Now, let's combine the constant terms and the \( x \) terms separately:
- For the constant terms: \( 4 - 16 = -12 \)
- For the \( x \) terms: \( 24x - 7x = 17x \)
Step 5: Write the final simplified expression
Putting it all together, we have: \[ 17x - 12 \]
Thus, the expression \( 4 + 8(3x - 2) - 7x \) simplifies to:
\[ \boxed{17x - 12} \]