To determine which equation matches the solution set of \( {5} \), we need to substitute \( x = 5 \) into each equation and check if they hold true.
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Equation: \( 3x + 4 = 7 \)
- Substitute \( x = 5 \): \[ 3(5) + 4 = 15 + 4 = 19 \quad \text{(not equal to 7)} \]
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Equation: \( x^2 - 10 = 15 \)
- Substitute \( x = 5 \): \[ 5^2 - 10 = 25 - 10 = 15 \quad \text{(true)} \]
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Equation: \( 2x - 20 = 30 \)
- Substitute \( x = 5 \): \[ 2(5) - 20 = 10 - 20 = -10 \quad \text{(not equal to 30)} \]
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Equation: \( x + x - 9 = 1 + x \)
- Substitute \( x = 5 \): \[ 5 + 5 - 9 = 1 + 5 \quad \Rightarrow \quad 10 - 9 = 6 \quad \Rightarrow \quad 1 + 5 = 6 \quad \text{(true)} \]
The equations that are true when substituting \( x = 5 \) are:
- \( x^2 - 10 = 15 \)
- \( x + x - 9 = 1 + x \)
However, to match the solution set \( {5} \), we are looking for an equation where \( 5 \) is the only solution.
The equation \( x^2 - 10 = 15 \) can be rewritten as: \[ x^2 - 25 = 0 \quad \Rightarrow \quad (x - 5)(x + 5) = 0 \] This has solutions \( x = 5 \) and \( x = -5 \), so it does not match the solution set \( {5} \).
The equation \( x + x - 9 = 1 + x \) simplifies to: \[ 2x - 9 = 1 + x \quad \Rightarrow \quad 2x - x = 10 \quad \Rightarrow \quad x = 10 \quad \text{(which is not true)} \]
Upon reevaluating, none of the equations provided yield a unique solution of \( x = 5 \) only.
Therefore, none of the provided options match the solution set of \( {5} \).