To solve: |3x−1|≻2 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: |3x−1|≻2 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.

Cristiano Sears · Accepted Answer

Calculation:  To solve: |3x−1|≻2  The given equation is of the form of |x|&amp;gt;k. However, the standard method for solving inequalities that involve absolute value cannot be applied to |3x−1|≻2 because k is negative.  We will solve the given equation |3x−1|≻2 by inspection.  |3x−1|≻2 is satisfied by all real numbers because the absolute value of (3x−1), regardless of what number is substituted for x, will always be greater than -1.  The solution set is the set of all real numbers, which we can express in interval notation as (−∞,∞).  Conclusion:  Absolute values are always greater or equal to zero. So |3x−1|≻2 is true for all x and the interval notation is (−∞,∞).

To solve:|3x-1|>-2General strategy to solve the inequalities tha

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