To determine how many of the equations have the solution set \({5}\), we will solve each equation separately and check if \(x = 5\), \(b = 5\), and \(h = 5\) satisfy them.
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Equation 1: \[ 2(x - 3) + 1 = 5 \] Simplifying the left side: \[ 2x - 6 + 1 = 5 \] \[ 2x - 5 = 5 \] \[ 2x = 10 \] \[ x = 5 \] \(x = 5\) is a solution.
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Equation 2: \[ 3b^{15} = 1 \] To isolate \(b\), divide both sides by 3: \[ b^{15} = \frac{1}{3} \] To solve for \(b\): \[ b = \left(\frac{1}{3}\right)^{\frac{1}{15}} \] This value is not equal to 5, so \(b = 5\) is not a solution.
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Equation 3: \[ 2h - 30 = 40 \] Adding 30 to both sides: \[ 2h = 70 \] Dividing by 2: \[ h = 35 \] This value is not equal to 5, so \(h = 5\) is not a solution.
Now, summarizing the results:
- Equation 1 has the solution \(x = 5\).
- Equation 2 does not have the solution \(b = 5\).
- Equation 3 does not have the solution \(h = 5\).
Only the first equation has the solution \(5\).
Therefore, the number of equations that have the solution set \({5}\) is 1.