To determine which equation matches the solution set of the equations you've listed, let's solve each of them one by one.
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Equation 1: \( x^2 - 10 = 15 \) \[ x^2 - 10 = 15 \ x^2 = 15 + 10 \ x^2 = 25 \ x = \pm 5 \] (Solution set is {-5, 5})
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Equation 2: \( \frac{3x}{5} + 4 = 7 \) \[ \frac{3x}{5} + 4 = 7 \ \frac{3x}{5} = 7 - 4 \ \frac{3x}{5} = 3 \ 3x = 15 \ x = 5 \] (Solution set is {5})
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Equation 3: \( 2x - 20 + 30x + x - 9 = 1 + x \) \[ 2x - 20 + 30x + x - 9 = 1 + x \ (2x + 30x + x - x) - 20 - 9 = 1 \ 32x - 29 = 1 \ 32x = 1 + 29 \ 32x = 30 \ x = \frac{30}{32} = \frac{15}{16} \] (Solution set is {\frac{15}{16}})
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Equation 4: \( x + x - 9 = 1 + x \) \[ x + x - 9 = 1 + x \ 2x - 9 = 1 + x \ 2x - x = 1 + 9 \ x = 10 \] (Solution set is {10})
Now, let's summarize the solution sets:
- Equation 1: {-5, 5}
- Equation 2: {5}
- Equation 3: {\frac{15}{16}}
- Equation 4: {10}
The equation that matches the solution set of {5} is Equation 2: \( \frac{3x}{5} + 4 = 7 \).
1 answer