Is 2(x−1)+18

Question

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.

Answer 1

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.