To determine how many of the given equations have the solution set \({5}\), we will solve each equation and see if \(x = 5\) is the only solution.
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Equation: \(2(x - 3) + 1 = 5\)
\(2(x - 3) + 1 = 5\)
Subtract 1 from both sides:
\(2(x - 3) = 4\)
Divide by 2:
\(x - 3 = 2\)
Add 3 to both sides:
\(x = 5\)
So, the solution set for this equation is \({5}\).
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Equation: \(\frac{3b}{15} = 1\)
Multiply both sides by 15:
\(3b = 15\)
Divide by 3:
\(b = 5\)
Therefore, the solution set for this equation is also \({5}\).
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Equation: \(2h - 30 = 40\)
Add 30 to both sides:
\(2h = 70\)
Divide by 2:
\(h = 35\)
Therefore, the solution set for this equation is \({35}\).
Now we summarize:
- The first equation gives a solution set of \({5}\).
- The second equation gives a solution set of \({5}\).
- The third equation gives a solution set of \({35}\).
Thus, the total number of equations that have the solution set \({5}\) is 2.
The number of equations that have the solution set {5} is 2.