Let's analyze each equation step by step to determine their solution sets.
Equation A:
\[ 3(4 - 5h) - 7 = -12 + 2h \] First, we simplify the left side: \[ 3(4 - 5h) = 12 - 15h \] So, \[ 12 - 15h - 7 = -12 + 2h \] This simplifies to: \[ 5 - 15h = -12 + 2h \] Now, combine like terms: \[ 5 + 12 = 15h + 2h \] which results in: \[ 17 = 17h \] Dividing by 17 gives: \[ h = 1 \]
Equation B:
\[ 2(p - 3) - 1 = 6p + 142 \] First, we simplify: \[ 2p - 6 - 1 = 6p + 142 \] This becomes: \[ 2p - 7 = 6p + 142 \] Rearranging the equation: \[ -7 - 142 = 6p - 2p \] This simplifies to: \[ -149 = 4p \] Dividing by 4 gives: \[ p = -\frac{149}{4} \]
Equation C:
\[ 23v - 3 + 83 = -1 \] Combine like terms: \[ 23v + 80 = -1 \] Now, isolate \(v\): \[ 23v = -1 - 80 \] This simplifies to: \[ 23v = -81 \] Dividing by 23 gives: \[ v = -\frac{81}{23} \]
Summary of Solutions:
- Equation A: \( h = 1 \)
- Equation B: \( p = -\frac{149}{4} \)
- Equation C: \( v = -\frac{81}{23} \)
Now let's analyze the statements:
- Tamara says A and C have the same solution. (False, \(1 \neq -\frac{81}{23}\))
- Payton says B and C have the same solution. (False, \(-\frac{149}{4} \neq -\frac{81}{23}\))
- Krish says all three have the same solution. (False)
- Haruki says that none of the equations have the same solution. (True)
Conclusion:
Haruki is correct. None of the equations have the same solution.
1 answer