Question

What is the expression 4+8(3x−2)−7x when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work. (4 points)

Answer 1

To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations, along with the distributive property. Here's how we can proceed:

1. **Apply the distributive property**: We first distribute the \( 8 \) to both terms inside the parentheses \( (3x - 2) \).

\[
8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16
\]

2. **Substitute back into the expression**: Replace \( 8(3x - 2) \) in the original expression.

\[
4 + (24x - 16) - 7x
\]

3. **Combine like terms**: Now, we combine the constant terms \( 4 \) and \( -16 \), as well as the \( x \) terms \( 24x \) and \( -7x \).

- For constants:
\[
4 - 16 = -12
\]

- For the \( x \) terms:
\[
24x - 7x = 17x
\]

4. **Put it all together**: Now we combine our results.

\[
-12 + 17x
\]

5. **Final answer**: The simplified expression is:

\[
17x - 12
\]

So, the final simplified expression is \( 17x - 12 \).