To solve: |x+6|&gt;0 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. General properties for solving inequalities that involve absolute value are 1) |x|&gt;k is equivalent to x&lt;−k or x&gt;k, where k is positive number. 2) |x|&lt;k is equivalent to x≻k and x&lt;k, where k is a positive number and we can write a conjunction such as x≻k and x&lt;k in the compact form −k&lt;x&lt;k. If k is a non positive number, we can determine the solution sets by inspection.

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To solve: |x+6|&amp;gt;0 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. General properties for solving inequalities that involve absolute value are 1) |x|&amp;gt;k is equivalent to x&amp;lt;−k or x&amp;gt;k, where k is positive number. 2) |x|&amp;lt;k is equivalent to x≻k and x&amp;lt;k, where k is a positive number and we can write a conjunction such as x≻k and x&amp;lt;k in the compact form −k&amp;lt;x&amp;lt;k. If k is a non positive number, we can determine the solution sets by inspection.

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Calculation: To solve: |x+6|&amp;gt;0 The given equation is of the form of |x|&amp;gt;k. From the property we know that |x+6|&amp;gt;0 is equivalent to x+6&amp;lt;0 or x+6&amp;gt;0 First we have to isolate the absolute value expression on one side of the inequality before solving the inequality, so we have to subtract 6 from both sides. x+6&amp;lt;0 x+6&amp;gt;0 x+6−6&amp;lt;0−6 or x+6−6&amp;gt;0−6 x&amp;lt;−6 x≻6 The solution is x&amp;lt;−6 or x≻6 The solution set is (−∞,−6)∪(−6,∞) Conclusion: The solution set is (−∞,−6)∪(−6,∞)

To solve:|x+6|>0General strategy to solve the inequalities that

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