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

Answer 1

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

1. Distribute the \( 8 \) to both terms inside the parentheses:

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

2. Substitute the distributed expression back into the original:

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

3. Now, combine like terms. Start with the constants:

   \[ 4 - 16 = -12 \]

   So the expression now looks like:

   \[ -12 + 24x - 7x \]

4. Next, combine the \( x \) terms:

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

5. Now, put it all together:

   \[ -12 + 17x \]

Thus, the simplified expression is

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