Question

What is the expression \(4+8\left(3x-2\right)-7x\) 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 and the distributive property step by step.

**Step 1: Distribute the \(8\)**

We need to distribute \(8\) to both terms inside the parentheses \(3x - 2\):

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

**Step 2: Substitute back into the expression**

Now we substitute \(24x - 16\) back into the original expression:

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

**Step 3: Combine like terms**

Next, we will rearrange and combine all the terms. First, we can rewrite the expression:

\[
= 4 - 16 + 24x - 7x
\]

Now, combine the constants \(4\) and \(-16\):

\[
4 - 16 = -12
\]

Then, combine the \(x\) terms \(24x - 7x\):

\[
24x - 7x = 17x
\]

**Step 4: Write the final simplified expression**

Putting it all together, we have:

\[
-12 + 17x
\]

Thus, the expression \(4 + 8(3x - 2) - 7x\) simplifies to:

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