To determine how many of the given equations have the solution set \({5}\), we will solve each equation step-by-step.
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Equation 1: \(2(x - 3) + 1 = 5\) \[ 2(x - 3) + 1 = 5 \] Subtract 1 from both sides: \[ 2(x - 3) = 4 \] Divide both sides by 2: \[ x - 3 = 2 \] Add 3 to both sides: \[ x = 5 \] Solution set is \({5}\).
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Equation 2: \(3b^{15} = 1\) To isolate \(b\), we divide both sides by 3: \[ b^{15} = \frac{1}{3} \] This equation states that \(b\) raised to the power of 15 equals \(\frac{1}{3}\). For \(b = 5\): \[ 5^{15} \neq \frac{1}{3} \] Thus, the solution for this equation is not \(5\). Solution set is not \({5}\).
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Equation 3: \(2h - 30 = 40\) Add 30 to both sides: \[ 2h = 70 \] Divide both sides by 2: \[ h = 35 \] The solution is not \(5\). Solution set is not \({5}\).
In summary, only the first equation has the solution set \({5}\). Therefore, the number of equations that have the solution set \({5}\) is:
\[ \boxed{1} \]