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 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 2

What’s the answer not simplified

Answer 3

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 4

So how do you simplify the answer

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