What is the minimum value of |x-4| + |x+6| + |x-5| ?	Choose the correct choice from the following answers
A) -3  B) 3  C) 5  D) 7  E) 11
A cannot be the answer as all the three terms are in modulus and hence the answer will be non negative.   |x-4| &gt;= 0 --&gt; Minimum occurs at x = 4   |x+6| &gt;= 0 --&gt; Minimum occurs at x = -6   |x-5| &gt;= 0 --&gt; Minimum occurs at x = 5   x = -6 --&gt; Result = 10 + 0 + 11= 
<gadget id="calculator">10 + 0 + 11</gadget>
<output>21</output>
21. Also any negative value will push the combined value of |x-4| + |x-5| to a value &gt; 9.   x= 4 --&gt; Result = 0 + 10 + 1= 
<gadget id="calculator">0 + 10 + 1</gadget>
<output>11</output>
11   x= 5 --&gt; Result = 1 + 11+ 0= 
<gadget id="calculator">1 + 11+ 0</gadget>
<output>12</output>
12   x= 6 --&gt; Result = 2 + 12 +1= 
<gadget id="calculator">2 + 12 +1</gadget>
<output>15</output>
15   So minimum value of the expression occurs at x= 4 and the resultant value = 11   Answer: 11
<result>E</result>
What is the minimum value of |x-4| + |x+6| + |x-5| ?