Question
Is 2(x−1)+18
equivalent to 6(x+3)−4x−6
? Use algebra to find your answer. Show your work and explain your answer. (4 points)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
equivalent to 6(x+3)−4x−6
? Use algebra to find your answer. Show your work and explain your answer. (4 points)
Math Short Answer Rubric (4 points)
Points Awarded Criteria
4
The answer is clear and correct.
The answer shows that the student used problem-solving skills and reasoning.
All work is shown or explained.
3
The answer is mostly correct. The student made small errors while solving.
The answer shows that the student used some problem-solving skills and reasoning.
Most work is shown or explained.
2
The answer is partially correct. The student made errors while solving.
The answer shows that the student used some problem-solving skills or reasoning.
Some work is shown or explained.
1
The answer is incorrect. The student made errors while solving.
The answer shows little problem-solving skills or reasoning.
Little or no work is shown.
0 The question is not answered.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To determine if the two expressions \(2(x-1)+18\) and \(6(x+3)-4x-6\) are equivalent, we need to simplify both expressions and then compare them. Let's start by simplifying each expression step by step.
### Simplifying the Left Expression
1. Write down the expression:
\[
2(x - 1) + 18
\]
2. Distribute \(2\) into the parentheses:
\[
2 \cdot x - 2 \cdot 1 + 18 = 2x - 2 + 18
\]
3. Combine like terms:
\[
2x + 16
\]
### Simplifying the Right Expression
1. Write down the expression:
\[
6(x + 3) - 4x - 6
\]
2. Distribute \(6\) into the parentheses:
\[
6 \cdot x + 6 \cdot 3 - 4x - 6 = 6x + 18 - 4x - 6
\]
3. Combine like terms:
- Combine \(6x - 4x\) to get \(2x\).
- Combine \(18 - 6\) to get \(12\).
So:
\[
2x + 12
\]
### Comparing the Two Expressions
Now we can compare the simplified forms of both expressions:
- Left Expression: \(2x + 16\)
- Right Expression: \(2x + 12\)
Since \(2x + 16\) is not equal to \(2x + 12\), we conclude that the two expressions are **not equivalent**.
### Conclusion
The final result shows:
\[
2(x-1) + 18 \neq 6(x+3) - 4x - 6
\]
Thus, the answer is **no**, the two expressions are not equivalent.
### Simplifying the Left Expression
1. Write down the expression:
\[
2(x - 1) + 18
\]
2. Distribute \(2\) into the parentheses:
\[
2 \cdot x - 2 \cdot 1 + 18 = 2x - 2 + 18
\]
3. Combine like terms:
\[
2x + 16
\]
### Simplifying the Right Expression
1. Write down the expression:
\[
6(x + 3) - 4x - 6
\]
2. Distribute \(6\) into the parentheses:
\[
6 \cdot x + 6 \cdot 3 - 4x - 6 = 6x + 18 - 4x - 6
\]
3. Combine like terms:
- Combine \(6x - 4x\) to get \(2x\).
- Combine \(18 - 6\) to get \(12\).
So:
\[
2x + 12
\]
### Comparing the Two Expressions
Now we can compare the simplified forms of both expressions:
- Left Expression: \(2x + 16\)
- Right Expression: \(2x + 12\)
Since \(2x + 16\) is not equal to \(2x + 12\), we conclude that the two expressions are **not equivalent**.
### Conclusion
The final result shows:
\[
2(x-1) + 18 \neq 6(x+3) - 4x - 6
\]
Thus, the answer is **no**, the two expressions are not equivalent.
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