To determine how many of the given equations have the solution set {5}, we will solve each equation and check if \(x = 5\), \(b = 5\), or \(h = 5\) is the only solution.
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For the equation \(2(x - 3) + 1 = 5\): \[ 2(x - 3) + 1 = 5 \] First, simplify: \[ 2x - 6 + 1 = 5 \] \[ 2x - 5 = 5 \] Add 5 to both sides: \[ 2x = 10 \] Divide by 2: \[ x = 5 \] The solution is \(x = 5\).
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For the equation \(3b + 15 = 1\): \[ 3b + 15 = 1 \] Subtract 15 from both sides: \[ 3b = 1 - 15 \] \[ 3b = -14 \] Divide by 3: \[ b = -\frac{14}{3} \] The solution is not \(b = 5\).
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For the equation \(2h - 30 = 40\): \[ 2h - 30 = 40 \] Add 30 to both sides: \[ 2h = 40 + 30 \] \[ 2h = 70 \] Divide by 2: \[ h = 35 \] The solution is not \(h = 5\).
In summary, only the first equation \(2(x - 3) + 1 = 5\) has the solution set {5}. Therefore, the total number of equations that have the solution set {5} is:
\[ \boxed{1} \]
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