What is the minimum value of |x-4| + |x+8| + |x-5| ? Options.
A) -13
B) 13
C) 5
D) 7
E) 8
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+8| &gt;= 0 --&gt; Minimum occurs at x = -8   |x-5| &gt;= 0 --&gt; Minimum occurs at x = 5   x = -8 --&gt; Result = 12 + 0 + 13= 
<gadget id="calculator">12 + 0 + 13</gadget>
<output>25</output>
25. Also any negative value will push the combined value of |x-4| + |x-5| to a value &gt; 9.   x= 4 --&gt; Result = 0 + 12 + 1= 
<gadget id="calculator">0 + 12 + 1</gadget>
<output>13</output>
13   x= 5 --&gt; Result = 1 + 13 + 0= 
<gadget id="calculator">1 + 13 + 0</gadget>
<output>14</output>
14   x= 8 --&gt; Result = 4 + 16 + 3= 
<gadget id="calculator">4 + 16 + 3</gadget>
<output>23</output>
23   So minimum value of the expression occurs at x= 4 and the resultant value = 13   Answer: 13
<result>B</result>
What is the minimum value of |x-4| + |x+8| + |x-5| ?