To determine how many of the given equations have the solution set {5}, we need to check if each equation is satisfied when \( x = 5 \).
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Equation: \( 2(x−3)+1=5 \)
Substitute \( x = 5 \): \[ 2(5−3)+1 = 2(2)+1 = 4+1 = 5 \] This equation is satisfied.
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Equation: \( 3b^{15}=1 \)
To solve for \( b \): \[ b^{15} = \frac{1}{3} \] \( b = \left(\frac{1}{3}\right)^{\frac{1}{15}} \). This does not equal 5, so this equation is not satisfied.
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Equation: \( 2h−30=40 \)
Substitute \( h = 5 \): \[ 2(5)−30 = 10−30 = -20 \neq 40 \] This equation is also not satisfied.
Now, let's summarize the results:
- The first equation is satisfied when \( x = 5 \).
- The second equation is not satisfied when \( b = 5 \).
- The third equation is not satisfied when \( h = 5 \).
Thus, only 1 equation has the solution set {5}.
Therefore, the number of equations that have the solution set {5} is 1.