Let's analyze the problem step by step.
Identifying the Property used to go from Line 2 to Line 3:
- From Line 2, \(3x + 1 = 17\) to Line 3, \(3x = 16\), the student performed a subtraction of 1 from both sides. The property used here is the subtraction property of equality.
Which line has a mistake?
- There is no mistake in Lines 1, 2, or 3. However, Line 4 states \(x = \frac{16}{3}\), which is incorrect. The correct simplification leads to \(x = \frac{16}{3}\). Thus, line 4 is where the answer is incorrect.
What should have been the correct answer for the equation?
- From Line 3, the correct answer is \(x = \frac{16}{3}\), which is approximately \(5.33\). This value is not listed in the provided options.
Given the options:
- Distributive property (not applicable here)
- Combine like terms (used in Line 1 to Line 2)
- Subtraction property of equality (correct for moving from Line 2 to Line 3, which we choose)
- Multiplication property of equality (not applicable here)
- Line 1 (no mistake)
- Line 2 (no mistake)
- Line 3 (no mistake)
- Line 4 (correct answer needed here)
- No solution (false)
- \(x = 5\) (false)
- \(x = 45\) (false)
- \(x = 15\) (false)
The responses should be:
- Property used: Subtraction property of equality
- Line with a mistake: Line 4
- Correct answer: Since the answer \(x = \frac{16}{3}\) is not listed, no response option fits. However, \(x = 5\) is approximately close but not accurate. If selecting among provided options, we note that there is no exact solution given.
So the best answers are:
- Property from Line 2 to Line 3: Subtraction property of equality
- Line with mistake: Line 4
- Correct answer: No solution (from provided options).
If a specific choice must be made despite the error, perhaps indicate \(x = 5\) is the closest numeric match resulting but clarify that it is incorrect in precise calculation.
1 answer