To determine how many of the given equations have the solution set {5}, we need to solve each equation individually and check if it yields the solution \( x = 5 \).
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Equation 1: \( 2(x - 3) + 1 = 5 \)
\[ 2(x - 3) + 1 = 5 \] \[ 2(x - 3) = 5 - 1 \] \[ 2(x - 3) = 4 \] \[ x - 3 = \frac{4}{2} \] \[ x - 3 = 2 \] \[ x = 2 + 3 \] \[ x = 5 \]
This equation has the solution \( x = 5 \).
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Equation 2: \( 3b = 15 \)
\[ 3b = 15 \] \[ b = \frac{15}{3} \] \[ b = 5 \]
This equation has the solution \( b = 5 \).
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Equation 3: \( 2h - 30 = 40 \)
\[ 2h - 30 = 40 \] \[ 2h = 40 + 30 \] \[ 2h = 70 \] \[ h = \frac{70}{2} \] \[ h = 35 \]
This equation does not have the solution \( h = 5 \).
Now, let's summarize the findings:
- Equation 1: Has \( x = 5 \)
- Equation 2: Has \( b = 5 \)
- Equation 3: Does not have \( h = 5 \)
Therefore, 2 out of the 3 equations have the solution set {5}.
The number of equations that have the solution set {5} is 2.