<PRE><B>Question 1144798</B>
&lt;br&gt;
{{{1/(x-1)&lt;5}}}&lt;br&gt;
Solution strategy: multiply both sides by (x-1) to clear fractions.&lt;br&gt;
Case 1: x-1 &lt; 0 (i.e., x &lt; 1)&lt;br&gt;
If x &lt; 1, (x-1) is negative, so multiplying by (x-1) reverses the direction of the inequality.&lt;br&gt;
{{{1 &gt; 5x-5}}}
{{{6 &gt; 5x}}}
{{{5x &lt; 6}}}
{{{x &lt; 6/5}}}&lt;br&gt;
So if x &lt; 1, an &quot;additional&quot; restriction is that x &lt; 6/5.  But ALL values of x that are less than 1 are less than 6/5.  So all numbers less than 1 are part of the solution set.&lt;br&gt;
Case 2: x-1 &gt; 0 (i.e., x &gt; 1)&lt;br&gt;
If x &gt; 1, (x-1) is positive, so multiplying by (x-1) does not change the direction of the inequality.&lt;br&gt;
{{{1 &lt; 5x-5}}}
{{{6 &lt; 5x}}}
{{{6/5 &lt; x}}}
{{{x &gt; 6/5}}}&lt;br&gt;
So if x &gt; 1, the additional restriction is that x &gt; 6/5.  So the other part of the solution set is all the number greater than 6/5 = 1.2.&lt;br&gt;
Final solution set: (-infinity, 1) union (1.2, infinity)</PRE>