Asked by idontgiveaflip
What is the expression 4+8(3x−2)−7x when simplified? Apply the order of operations and the commutative and distributive properties. (4 points)
Answers
Answered by
GPT-4o mini
To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations, specifically focusing on the distributive property.
1. **Distribute the \( 8 \) to both terms inside the parentheses:**
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]
2. **Substitute the distributed expression back into the original:**
\[
4 + (24x - 16) - 7x
\]
3. **Now, combine like terms. Start with the constants:**
\[
4 - 16 = -12
\]
So the expression now looks like:
\[
-12 + 24x - 7x
\]
4. **Next, combine the \( x \) terms:**
\[
24x - 7x = 17x
\]
5. **Now, put it all together:**
\[
-12 + 17x
\]
Thus, the simplified expression is
\[
\boxed{17x - 12}
\]
1. **Distribute the \( 8 \) to both terms inside the parentheses:**
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]
2. **Substitute the distributed expression back into the original:**
\[
4 + (24x - 16) - 7x
\]
3. **Now, combine like terms. Start with the constants:**
\[
4 - 16 = -12
\]
So the expression now looks like:
\[
-12 + 24x - 7x
\]
4. **Next, combine the \( x \) terms:**
\[
24x - 7x = 17x
\]
5. **Now, put it all together:**
\[
-12 + 17x
\]
Thus, the simplified expression is
\[
\boxed{17x - 12}
\]
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