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.

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.

Answer 1

To simplify the expression 4 + 8(3x - 2) - 7x, we begin by simplifying the expression within the parentheses.

3x - 2

Next, we distribute the 8 to each term within the parentheses:
8 * 3x - 8 * 2
24x - 16

Now, substituting the simplified expression back into the original equation, we have:
4 + 24x - 16 - 7x

Next, we combine like terms:
(24x - 7x) + (4 - 16)
17x - 12

Therefore, the simplified expression is 17x - 12.

Answer 2

To simplify the expression 4+8(3x−2)−7x, we need to apply the order of operations (also known as PEMDAS) which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

First, we need to simplify the expression within the parentheses: 3x - 2.

Now, let's distribute the 8 to each term inside the parentheses: 8 * 3x - 8 * 2.

That gives us: 24x - 16.

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

Next, we need to combine like terms. We can start by combining the -16 and 4: -16 + 4 = -12.

So, we have: (24x - 12) - 7x.

Now, we can simplify further by combining the x terms: 24x - 7x = 17x.

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

Therefore, the simplified expression is 17x - 12.

Answer 3

To simplify the expression 4 + 8(3x-2) - 7x, we need to apply the order of operations as well as the commutative and distributive properties. Let's break it down step by step:

Step 1: Simplify inside the parentheses.
We start by applying the distributive property, which states that we need to multiply the number outside the parentheses with each term inside the parentheses. In this case, we have 8 times (3x-2):

8 * 3x = 24x
8 * (-2) = -16

So, the expression becomes: 4 + 24x - 16 - 7x.

Step 2: Combine like terms.
Now, we combine the terms that have the same variable (in this case, x) by adding or subtracting their coefficients:

24x - 7x = 17x

So, the expression simplifies further: 4 + 17x - 16.

Step 3: Combine the remaining terms.
Now we combine the terms that do not have a variable. In this case, we have 4 and -16:

4 - 16 = -12

So, the expression simplifies even further: -12 + 17x.

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