To determine whose statements about the equations are correct, we will need to solve each of the equations and identify their solution sets.
Equation A:
\(3(4 - 5h) - 7 = -12 + 2h\)
- Distribute on the left side: \(12 - 15h - 7 = -12 + 2h\)
- Simplify: \(5 - 15h = -12 + 2h\)
- Rearrange to isolate \(h\):
\(5 + 12 = 15h + 2h\)
\(17 = 17h\)
\(h = 1\)
Solution Set of Equation A: \( h = 1 \)
Equation B:
\(2(p - 3) - 1 = 6p + 142\)
- Distribute on the left side: \(2p - 6 - 1 = 6p + 142\)
- Simplify: \(2p - 7 = 6p + 142\)
- Rearrange to isolate \(p\):
\(-7 - 142 = 6p - 2p\)
\(-149 = 4p\)
\(p = -\frac{149}{4}\)
Solution Set of Equation B: \( p = -\frac{149}{4} \)
Equation C:
\(23v - 3 + 83 = -1\)
- Combine like terms: \(23v + 80 = -1\)
- Rearrange to isolate \(v\):
\(23v = -1 - 80\)
\(23v = -81\)
\(v = -\frac{81}{23}\)
Solution Set of Equation C: \( v = -\frac{81}{23} \)
Now let's summarize the solutions:
- Equation A has the solution \( h = 1 \).
- Equation B has the solution \( p = -\frac{149}{4} \).
- Equation C has the solution \( v = -\frac{81}{23} \).
Now, we can analyze the statements:
- Tamara: "Equation A and Equation C have the same solution." - False (Solutions are \(h = 1\) and \(v = -\frac{81}{23}\)).
- Payton: "Equation B and Equation C have the same solution." - False (Solutions are \(p = -\frac{149}{4}\) and \(v = -\frac{81}{23}\)).
- Krish: "All three have the same solution." - False (All three equations have different solutions).
- Haruki: "None of the equations have the same solution." - True (All three equations have different solutions).
Based on this analysis, the correct answer is Haruki.
1 answer