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

What’s the answer not simplified

Answer 2

So how do you simplify the answer

Answer 3

To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations and use the distributive property step by step. Here’s how it goes:

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

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

3. **Combine like terms**. Start by grouping the constant terms and the terms with \( x \):
- For the constant terms: \( 4 - 16 = -12 \)
- For the \( x \) terms: \( 24x - 7x = 17x \)

4. **Putting it all together**:
\[
17x - 12
\]

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

Answer 4

If you want the expression \( 4 + 8(3x - 2) - 7x \) without simplifying it (i.e., in its step-by-step form before final simplification), we look at the original expression and apply the distributive property but stop before combining like terms.

Starting with the expression:
\[
4 + 8(3x - 2) - 7x
\]

Applying the distributive property:
1. Distribute \( 8 \) to \( (3x - 2) \):
\[
4 + 24x - 16 - 7x
\]

At this point, the expression \( 4 + 24x - 16 - 7x \) is the result before combining like terms.

In this form, you would keep it as:
\[
4 + 24x - 16 - 7x
\]

So, the answer not simplified is:
\[
\boxed{4 + 24x - 16 - 7x}
\]

Answer 5

To simplify the expression \( 4 + 24x - 16 - 7x \), follow these steps:

1. **Combine like terms**:
- First, combine the constant terms:
\[
4 - 16 = -12
\]
- Next, combine the \( x \) terms:
\[
24x - 7x = 17x
\]

2. **Rewrite the expression with the combined terms**:
\[
17x - 12
\]

Thus, the expression \( 4 + 24x - 16 - 7x \) simplifies to:
\[
\boxed{17x - 12}
\]