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 ur work

Answer 1

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:

\[
\boxed{17x - 12}
\]