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(D) The given inequality is $|x-2| \geq 8.$ By the property of absolute value inequalities,$|u| \geq a$ implies $u \leq -a$ or $u \geq a.$ Applying th

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$x \in (-\infty, -6] \cup [10, \infty)$

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(D) The given inequality is $|x-2| \geq 8.$ By the property of absolute value inequalities,$|u| \geq a$ implies $u \leq -a$ or $u \geq a.$ Applying this to the given expression: $x-2 \leq -8$ or $x-2 \geq 8.$ Solving the first part: $x \leq -8 + 2$ $x \leq -6.$ Solving the second part: $x \geq 8 + 2$ $x \geq 10.$ Combining these intervals,we get $x \in (-\infty, -6] \cup [10, \infty).$ Thus,the correct option is $D.$

If $|x-2| \geq 8,$ then...

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