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 \( 17x - 12 \).