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. (In kids words please)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 4 + 8(3x - 2) - 7x, we follow the order of operations which tells us to solve the parts inside parentheses first.

First, we simplify the expression inside the parentheses:
3x - 2

Next, we multiply 8 with the simplified expression:
8 * (3x - 2) = 24x - 16

So now our expression becomes:
4 + 24x - 16 - 7x

Next, we use the commutative property to rearrange the terms so that we can add and subtract them easily:
4 - 16 + 24x - 7x

Then, we combine like terms, which means we add or subtract terms with the same variable and exponent:
(-16 + 4) + (24x - 7x)

-16 + 4 = -12 (Two negatives make a positive)
24x - 7x = 17x

Now our expression is simplified to:
-12 + 17x

Therefore, the simplified expression is -12 + 17x.

Answer 2

Can you make it shorter

Answer 3

[AI-generated answer — Bot GPT 3.5]

Certainly! The expression 4 + 8(3x - 2) - 7x simplifies to -12 + 17x.

Answer 4

[AI-generated answer — Explain Bot]

Sure! Let's simplify the expression 4 + 8(3x - 2) - 7x step-by-step using the order of operations and the properties you mentioned.

1. Start by simplifying the expression inside the parentheses (3x - 2) first.
8 * (3x - 2) means we multiply 8 by everything inside the parentheses.
So, we get: 8 * 3x - 8 * 2

This simplifies to: 24x - 16

2. Now, substitute the simplified expression (24x - 16) back into our original expression:
4 + (24x - 16) - 7x

3. Next, perform the multiplications and additions/subtractions in order, working from left to right.

Adding 4 and -16: 4 - 16 = -12

So, our expression becomes: -12 + 24x - 7x

4. Combine the like terms, which means adding together the terms with the same variable (x) raised to the same power (1):

The terms with x are 24x and -7x, so we add them together:
24x - 7x = 17x

Now our simplified expression is: -12 + 17x

And that's the final answer! The expression 4 + 8(3x - 2) - 7x simplifies to -12 + 17x.