Question

what is the expression 4+8(3x-2)-7x when simplified? apply the order of operations and the commuitve and distributive properties show all your work.

Answer 1

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:

1. **Distributive Property**: First, we need to apply the distributive property to the term \( 8(3x - 2) \):
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]

2. **Substituting Back into the Expression**: Now we can substitute \( 24x - 16 \) back into the original expression:
\[
4 + (24x - 16) - 7x
\]

3. **Combining Like Terms**: Next, combine the constant terms and the variable terms:
- First, combine the constants: \( 4 - 16 = -12 \)
- Then combine the \( x \) terms: \( 24x - 7x = 17x \)

4. **Final Expression**: Putting it all together, we get:
\[
17x - 12
\]

So, the simplified expression is:
\[
\boxed{17x - 12}
\]