What is the minimum value of |x-4| + |x+7| + |x-5| ?
Choose the most appropriate option:  A) -3  B) 3  C) 5  D) -12  E) 12
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+7| &gt;= 0 --&gt; Minimum occurs at x = -7   |x-5| &gt;= 0 --&gt; Minimum occurs at x = 5   x = -7 --&gt; Result = 11 + 0 + 12= 
<gadget id="calculator">11 + 0 + 12</gadget>
<output>23</output>
23. Also any negative value will push the combined value of |x-4| + |x-5| to a value &gt; 9.   x= 4 --&gt; Result = 0 + 11 + 1= 
<gadget id="calculator">0 + 11 + 1</gadget>
<output>12</output>
12   x= 5 --&gt; Result = 1 + 12 + 0= 
<gadget id="calculator">1 + 12 + 0</gadget>
<output>13</output>
13   x= 7 --&gt; Result = 3 + 14 + 2= 
<gadget id="calculator">3 + 14 + 2</gadget>
<output>19</output>
19   So minimum value of the expression occurs at x= 4 and the resultant value = 12   Answer: 12
<result>E</result>
What is the minimum value of |x-4| + |x+7| + |x-5| ?