A manufacturer of a certain type of screw rejects any screw whose length is less than 2.47 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?
Choose the correct choice from the following choices:  A) |k + 0.03| > 2.5  B) |k — 0.03| <= 2.5  C) |k — 2.5| > 0.03  D) |k — 2.5| >= 0.06  E) 2|k — 2.5| <= 0.06
So, let's go through this step by step:   rejects any screw whose length is less than 2.47 centimeters or greater than 2.5 + 0.03 centimeters.   In other words, any screw that is less than: 2.47 or greater than   2.50 + 0.03= 
<gadget id="calculator">  2.50 + 0.03</gadget>
<output>2.53</output>
2.53will be rejected.   If k represents the length of a screw   In other words, K is an acceptable screw that must fall within the acceptable range of 2.47 to 2.53, So:   2.47 ≤ K ≤ 2.53   You can rule out answers with &lt; or &gt; as opposed to ≤ or ≥ because the length cannot be LESS than 2.47 or GREATER than 2.53. In other words, 2.47 and 2.53 are acceptable lengths.   Let's look at (2|k — 2.5| &lt;= 0.06):   2|k — 2.5| &lt;= 0.06 or |k — 2.5| &lt;= 0.03   For the positive case: k - 2.5 ≤ 0.03 ===&gt;k ≤ 2.53   For the negative case: -(k - 2.5) ≤ 0.03 ===&gt; -k +2.5 ≤ 0.03 ===&gt; - k ≤ -2.47 ===&gt;k ≥ 2.47   2.47 ≤ k ≤ 2.53   (2|k — 2.5| &lt;= 0.06)
<result>E</result>
A manufacturer of a certain type of screw rejects any screw whose length is less than 2.47 centimeters or greater than 2.5 + 0.03 centimeters. If k represents the length of a screw, in centimeters, which of the following inequalities specifies all the lengths of screws that are acceptable?