What is the expression 4+8(3x−2)−7x

Question

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 follow the order of operations and apply the distributive property.

Step 1: Distribute the \(8\) into the parentheses

The expression inside the parentheses is \(3x - 2\). We will use the distributive property to multiply \(8\) by each term inside the parentheses:

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

Step 2: Substitute back into the expression

Now, we substitute \(24x - 16\) back into the original expression:

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

Step 3: Combine like terms

Next, we can simplify the expression by combining like terms. Start by rewriting it clearly:

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

Now, combine the constant terms (\(4 - 16\)) and the \(x\) terms (\(24x - 7x\)):

1. Constant terms: \[ 4 - 16 = -12 \]

2. Like terms (with x): \[ 24x - 7x = 17x \]

Step 4: Write the final simplified expression

Combining both results, we have:

\[ -12 + 17x \]

To write it in standard form, we can express it as:

\[ 17x - 12 \]

Final Answer

The simplified expression is:

\[ 17x - 12 \]