Question

Tamara, Payton, Krish, and Haruki are analyzing the solution sets to the following linear equations. Tamara says that Equation A and Equation C have the same solution. Payton says Equation B and Equation C have the same solution. Krish says all three have the same solution. Haruki says that none of the equations have the same solution. Identify who is correct about the linear equations. Equation A: 3(4−5h)−7=−12+2h Equation B: 2(p−3)−1=6p+142 Equation C: 23v−3+83=−1 Tamara Haruki Payton Krish

Answer 1

Is this correct?

Answer 2

Thank you, now please shut up for good

Answer 3

To determine who is correct about the solution sets of the equations, we need to solve each equation and see if they have the same solutions.

**Equation A:**
\[ 3(4−5h)−7=−12+2h \]

1. Distribute on the left side:
\[ 12 - 15h - 7 = -12 + 2h \]
\[ 5 - 15h = -12 + 2h \]

2. Add \(15h\) to both sides:
\[ 5 = -12 + 17h \]

3. Add \(12\) to both sides:
\[ 17 = 17h \]

4. Divide by \(17\):
\[ h = 1 \]

**Equation B:**
\[ 2(p−3)−1=6p+142 \]

1. Distribute on the left side:
\[ 2p - 6 - 1 = 6p + 142 \]
\[ 2p - 7 = 6p + 142 \]

2. Subtract \(2p\) from both sides:
\[ -7 = 4p + 142 \]

3. Subtract \(142\) from both sides:
\[ -149 = 4p \]

4. Divide by \(4\):
\[ p = -\frac{149}{4} \]

**Equation C:**
\[ 23v−3+83=−1 \]

1. Combine the constants on the left side:
\[ 23v + 80 = -1 \]

2. Subtract \(80\) from both sides:
\[ 23v = -81 \]

3. Divide by \(23\):
\[ v = -\frac{81}{23} \]

Now that we have the values:
- From Equation A, we have \(h = 1\).
- From Equation B, we have \(p = -\frac{149}{4}\).
- From Equation C, we have \(v = -\frac{81}{23}\).

Now, we analyze the statements:
- **Tamara** states that Equation A and Equation C have the same solution. (False, \(h \neq v\))
- **Payton** states that Equation B and Equation C have the same solution. (False, \(p \neq v\))
- **Krish** states that all three have the same solution. (False)
- **Haruki** states that none of the equations have the same solution. (True)

Thus, the only correct statement is **Haruki**.

Answer 4

Let's review the solutions carefully to ensure accuracy.

We have the three equations:

### **Equation A:**
\[ 3(4−5h)−7=−12+2h \]

1. Distribute:
\[ 12 - 15h - 7 = -12 + 2h \]
\[ 5 - 15h = -12 + 2h \]

2. Add \(15h\) to both sides:
\[ 5 = -12 + 17h \]

3. Add \(12\) to both sides:
\[ 17 = 17h \]

4. Divide by \(17\):
\[ h = 1 \]

### **Equation B:**
\[ 2(p−3)−1=6p+142 \]

1. Distribute:
\[ 2p - 6 - 1 = 6p + 142 \]
\[ 2p - 7 = 6p + 142 \]

2. Subtract \(2p\) from both sides:
\[ -7 = 4p + 142 \]

3. Subtract \(142\) from both sides:
\[ -149 = 4p \]

4. Divide by \(4\):
\[ p = -\frac{149}{4} \]

### **Equation C:**
\[ 23v−3+83=−1 \]

1. Combine the constants:
\[ 23v + 80 = -1 \]

2. Subtract \(80\) from both sides:
\[ 23v = -81 \]

3. Divide by \(23\):
\[ v = -\frac{81}{23} \]

### Summary of the Solutions:
- **From Equation A**: \( h = 1 \)
- **From Equation B**: \( p = -\frac{149}{4} \)
- **From Equation C**: \( v = -\frac{81}{23} \)

### Checking the Statements:
1. **Tamara**: Says Equation A and Equation C have the same solution. (False: \(h = 1\) and \(v = -\frac{81}{23}\))
2. **Payton**: Says Equation B and Equation C have the same solution. (False: \(p = -\frac{149}{4}\) and \(v = -\frac{81}{23}\))
3. **Krish**: Says all three have the same solution. (False)
4. **Haruki**: Says none of the equations have the same solution. (True)

### Conclusion:
The analysis confirms that **Haruki** is correct. None of the equations have the same solution, while Tamara, Payton, and Krish are incorrect. Thank you for your patience while we verified this!

Answer 5

I understand, and I appreciate your feedback. If you have any more questions in the future or need assistance, feel free to ask. Have a great day!