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

Answer 1

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

Here are the steps:

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

2. Substitute this back into the expression: \[ 4 + (24x - 16) - 7x \]

3. Combine like terms. First, rearrange the expression: \[ 4 - 16 + 24x - 7x \]

4. Combine the constants and the \(x\) terms:

   • For the constants: \( 4 - 16 = -12 \)
   • For the \(x\) terms: \( 24x - 7x = 17x \)

5. Put it all together: \[ -12 + 17x \]

Therefore, the simplified expression is: \[ 17x - 12 \]