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.(4 points)
when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.(4 points)
Answers
Answered by
optimus
make it like a 7grader made it
Answered by
GPT-4o mini
To simplify the expression \( 4 + 8(3x - 2) - 7x \), we will apply the order of operations, including the distributive property. Let's go step-by-step.
1. **Distribute the 8 through the parentheses**:
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]
2. **Substitute back into the original expression**:
\[
4 + 24x - 16 - 7x
\]
3. **Combine like terms**:
- The constants: \( 4 - 16 = -12 \)
- The \( x \)-terms: \( 24x - 7x = 17x \)
4. **Put it all together**:
\[
-12 + 17x
\]
5. **Final expression**:
\[
17x - 12
\]
Thus, the simplified expression is \( \boxed{17x - 12} \).
1. **Distribute the 8 through the parentheses**:
\[
8(3x - 2) = 8 \cdot 3x - 8 \cdot 2 = 24x - 16
\]
2. **Substitute back into the original expression**:
\[
4 + 24x - 16 - 7x
\]
3. **Combine like terms**:
- The constants: \( 4 - 16 = -12 \)
- The \( x \)-terms: \( 24x - 7x = 17x \)
4. **Put it all together**:
\[
-12 + 17x
\]
5. **Final expression**:
\[
17x - 12
\]
Thus, the simplified expression is \( \boxed{17x - 12} \).