To find which equation matches the solution set of {5}, we will substitute \( x = 5 \) into each equation and see which one holds true.
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Equation: \( 2x - 20 = 30 \)
Substituting \( x = 5 \): \[ 2(5) - 20 = 10 - 20 = -10 \quad \text{(not equal to } 30\text{)} \]
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Equation: \( x + x - 9 = 1 + x \)
Simplifying: \[ 2x - 9 = 1 + x \] Substituting \( x = 5 \): \[ 2(5) - 9 = 1 + 5 \implies 10 - 9 = 6 \implies 1 \neq 6 \quad \text{(not true)} \]
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Equation: \( \frac{3x}{5} + 4 = 7 \)
Substituting \( x = 5 \): \[ \frac{3(5)}{5} + 4 = 7 \implies 3 + 4 = 7 \quad \text{(true)} \]
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Equation: \( x^2 - 10 = 15 \)
Substituting \( x = 5 \): \[ 5^2 - 10 = 15 \implies 25 - 10 = 15 \quad \text{(true)} \]
Now let's summarize the results:
- Equation 1: \( 2x - 20 = 30 \) (Not true)
- Equation 2: \( x + x - 9 = 1 + x \) (Not true)
- Equation 3: \( \frac{3x}{5} + 4 = 7 \) (True)
- Equation 4: \( x^2 - 10 = 15 \) (True)
Thus, the equations that match the solution set of \({5}\) are:
- \( \frac{3x}{5} + 4 = 7 \)
- \( x^2 - 10 = 15 \)
However, if the task is to select only one, the equation that directly results in the solution set {5} is better represented by the more straightforward and linear equation:
Final Answer: \( \frac{3x}{5} + 4 = 7 \)
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