To solve: |x−2|&gt;6 General strategy to solve the inequalities that involve absolute value: Absolute value inequalities deal with the inequalities (&lt;,&gt;,≤,and≥) on the expressions with absolute sign. We can use the property |x|&gt;k is equivalent to x&lt;−k or x&gt;k, where k is a positive number When solving an absolute value inequality it's necessary to first isolate the absolure value expression on one side of the inequality before solving the inequality. |ax+b|&lt;c, where c&gt;0 =−c&lt;ax+b&lt;c |ax+b|&gt;c, where c&gt;0 =ax+b&lt;−c or ax+b&gt;c We can replace &gt; above with ≥ and&lt;with≤.

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To solve: |x−2|&amp;gt;6 General strategy to solve the inequalities that involve absolute value: Absolute value inequalities deal with the inequalities (&amp;lt;,&amp;gt;,≤,and≥) on the expressions with absolute sign. We can use the property |x|&amp;gt;k is equivalent to x&amp;lt;−k or x&amp;gt;k, where k is a positive number When solving an absolute value inequality it&#039;s necessary to first isolate the absolure value expression on one side of the inequality before solving the inequality. |ax+b|&amp;lt;c, where c&amp;gt;0 =−c&amp;lt;ax+b&amp;lt;c |ax+b|&amp;gt;c, where c&amp;gt;0 =ax+b&amp;lt;−c or ax+b&amp;gt;c We can replace &amp;gt; above with ≥ and&amp;lt;with≤.

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Calculation:  To solve: |x−2|&amp;gt;6  The number, x−2, must be more than 6 units away from zero.  Thus, |x−2|&amp;gt;6 is equivalent to x−2&amp;lt;−6 or x−2&amp;gt;6  Now we have to solve the above disjunction.  First we have to isolate the absolute value expression on one side of the inequality before solving the inequality, so we have to add 2 to both sides.  x−2&amp;lt;−6 x−2&amp;gt;6  x−2+2&amp;lt;−6+2 or x−2+2&amp;gt;6+2  x&amp;lt;−4 x&amp;gt;8  The solution set is (−∞,−4)∪(8,∞)  Conclusion:  The solution set is (−∞,−4)∪(8,∞)

To solve:|x-2|>6General strategy to solve the inequalities that

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