To find which equation has the solution set of {5}, we need to substitute \( x = 5 \) into each equation and see if the equation holds true.
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Equation 1: \( x^2 - 10 = 15 \)
Substitute \( x = 5 \): \[ 5^2 - 10 = 25 - 10 = 15 \quad \text{(True)} \]
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Equation 2: \( x + x - 9 = 1 + x \)
Substitute \( x = 5 \): \[ 5 + 5 - 9 = 1 + 5 \ 1 = 6 \quad \text{(False)} \]
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Equation 3: \( 2x - 20 = 30 \)
Substitute \( x = 5 \): \[ 2(5) - 20 = 30 \ 10 - 20 = 30 \ -10 = 30 \quad \text{(False)} \]
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Equation 4: \( 3x + 4 = 7 \)
Substitute \( x = 5 \): \[ 3(5) + 4 = 7 \ 15 + 4 = 7 \ 19 = 7 \quad \text{(False)} \]
Only the first equation \( x^2 - 10 = 15 \) holds true when \( x = 5 \). Therefore, the equation that matches the solution set of {5} is:
x^2 - 10 = 15.