To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will use the order of operations and the distributive property. Let's go through the steps carefully!
Step 1: Distribute the 8
First, we will distribute the \( 8 \) in the term \( 8(3x - 2) \):
\[ 8(3x) - 8(2) \]
Calculating that gives:
\[ 24x - 16 \]
Step 2: Rewrite the expression
Now, replace \( 8(3x - 2) \) in the original expression:
\[ 4 + (24x - 16) - 7x \]
Step 3: Combine like terms
Next, we combine all the constant terms and the terms with \( x \).
Constants:
- \( 4 - 16 = -12 \)
Terms with \( x \):
- \( 24x - 7x = 17x \)
Step 4: Write the simplified expression
Putting it all together gives us:
\[ 17x - 12 \]
Conclusion
So, the expression \( 4 + 8(3x - 2) - 7x \) simplified is:
\[ \boxed{17x - 12} \]