Let's solve each of the equations for \( x \):
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For the equation \( x - 6 = -16 \): \[ x = -16 + 6 = -10 \]
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For the equation \( x + 25 = 2 \): \[ x = 2 - 25 = -23 \]
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For the equation \( x + 19 = -5 \): \[ x = -5 - 19 = -24 \]
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For the equation \( x - 7 = 28 \): \[ x = 28 + 7 = 35 \]
Now, let's summarize the solutions:
- From the first equation: \( x = -10 \)
- From the second equation: \( x = -23 \)
- From the third equation: \( x = -24 \)
- From the fourth equation: \( x = 35 \)
Among \( -10, -23, -24, \) and \( 35 \), the solution with the lowest value is \( -24 \) from the equation \( x + 19 = -5 \).