To determine how many of the given equations have the solution set {5}, we will solve each equation for the variable.
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Equation: \(2(x - 3) + 1 = 5\)
Solve for \(x\): \[ 2(x - 3) + 1 = 5 \] \[ 2(x - 3) = 4 \quad \text{(subtracting 1 from both sides)} \] \[ x - 3 = 2 \quad \text{(dividing both sides by 2)} \] \[ x = 5 \quad \text{(adding 3 to both sides)} \]
This equation has the solution \(x = 5\).
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Equation: \(3b^{15} = 1\)
Solve for \(b\): \[ b^{15} = \frac{1}{3} \quad \text{(dividing both sides by 3)} \] To find \(b\): \[ b = \left( \frac{1}{3} \right)^{\frac{1}{15}} \]
The value of \(b\) is not \(5\). So this equation does not have the solution \(b = 5\).
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Equation: \(2h - 30 = 40\)
Solve for \(h\): \[ 2h = 70 \quad \text{(adding 30 to both sides)} \] \[ h = 35 \quad \text{(dividing both sides by 2)} \]
This equation does not have the solution \(h = 5\).
Now, let's summarize the results:
- The first equation has the solution \(x = 5\).
- The second equation has the solution \(b \approx 0.464\) (which is not 5).
- The third equation has the solution \(h = 35\) (which is not 5).
Thus, only 1 equation has the solution set {5}.
The number of equations that have the solution set {5} is 1.
1 answer