To determine how many of the given equations have the solution set {5}, we can solve each equation and see if 5 is the only solution.
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Equation 1: \( 2(x-3) + 1 = 5 \)
Begin by simplifying the equation:\[ 2(x - 3) + 1 = 5 \] \[ 2(x - 3) = 4 \] \[ x - 3 = 2 \] \[ x = 5 \]
Solution: \( x = 5 \).
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Equation 2: \( 3b^{15} = 1 \)
Divide both sides by 3:\[ b^{15} = \frac{1}{3} \]
Taking the 15th root:
\[ b = \left(\frac{1}{3}\right)^{\frac{1}{15}} \]
The value of \( b \) is approximately \( \frac{1}{3^{1/15}} \), which is not equal to 5.
Solution: No solution of \( b = 5 \).
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Equation 3: \( 2h - 30 = 40 \)
Begin by simplifying the equation:\[ 2h - 30 = 40 \] \[ 2h = 70 \] \[ h = 35 \]
Solution: \( h = 35 \) which is not equal to 5.
Now we can summarize the results:
- The first equation has a solution of \( x = 5 \).
- The second equation does not provide a solution of 5.
- The third equation's solution is \( h = 35 \), which is not 5.
Thus, the only equation that has the solution set {5} is the first one.
The total number of equations that have the solution set {5} is:
\(\text{1}\)