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
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GPT-4o mini
To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will follow the order of operations and apply the distributive property.
### Step 1: Apply the Distributive Property
First, we need to distribute \( 8 \) to both terms inside the parentheses \( (3x - 2) \).
\[
8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16
\]
### Step 2: Substitute Back into the Expression
Now we can substitute \( 24x - 16 \) back into the original expression:
\[
4 + 24x - 16 - 7x
\]
### Step 3: Combine Like Terms
Now, we will combine the constant terms and the coefficients of \( x \).
First, combine the constant terms:
\[
4 - 16 = -12
\]
Next, combine the \( x \)-terms:
\[
24x - 7x = 17x
\]
### Final Expression
Now we can rewrite the simplified expression by putting it all together:
\[
17x - 12
\]
Thus, the simplified expression for \( 4 + 8(3x - 2) - 7x \) is:
\[
\boxed{17x - 12}
\]
### Step 1: Apply the Distributive Property
First, we need to distribute \( 8 \) to both terms inside the parentheses \( (3x - 2) \).
\[
8(3x - 2) = 8 \cdot 3x + 8 \cdot (-2) = 24x - 16
\]
### Step 2: Substitute Back into the Expression
Now we can substitute \( 24x - 16 \) back into the original expression:
\[
4 + 24x - 16 - 7x
\]
### Step 3: Combine Like Terms
Now, we will combine the constant terms and the coefficients of \( x \).
First, combine the constant terms:
\[
4 - 16 = -12
\]
Next, combine the \( x \)-terms:
\[
24x - 7x = 17x
\]
### Final Expression
Now we can rewrite the simplified expression by putting it all together:
\[
17x - 12
\]
Thus, the simplified expression for \( 4 + 8(3x - 2) - 7x \) is:
\[
\boxed{17x - 12}
\]
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