The expression \( \sqrt{-(6 - x)} \) involves a square root, and for the square root to be defined in the real number system, the expression inside the square root must be non-negative. Therefore, we need to ensure that:
\[ -(6 - x) \geq 0 \]
This can be rearranged as follows:
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Multiply both sides by -1 (remember to reverse the inequality sign): \[ 6 - x \leq 0 \]
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Rearranging gives: \[ 6 \leq x \] or \[ x \geq 6 \]
Thus, the expression \( \sqrt{-(6 - x)} \) is defined for values of \( x \) that are greater than or equal to 6.
In interval notation, the solution is: \[ [6, \infty) \]
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