Question

What is the expression 4+8(3x−2)−7x when simplified? Apply the order of operations and the commutative and distributive properties. write it down. (4 points)

Answer 1

To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations, and use the distributive property.

Here are the steps:

1. **Distribute the 8 across the terms in the parentheses:**
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]

2. **Substitute this back into the expression:**
\[
4 + (24x - 16) - 7x
\]

3. **Combine like terms. First, rearrange the expression:**
\[
4 - 16 + 24x - 7x
\]

4. **Combine the constants and the \(x\) terms:**
- For the constants: \( 4 - 16 = -12 \)
- For the \(x\) terms: \( 24x - 7x = 17x \)

5. **Put it all together:**
\[
-12 + 17x
\]

Therefore, the simplified expression is:
\[
17x - 12
\]