<p>"A regulation for riding a certain amusement park ride requires that a child be between 30 inches and 50 inches tall. which of the following inequalities can be used to determine whether or not a child's height h satisfied the regulation for this ride?</p>
<p>I eliminated the answer choices to C, and D</p>
<p>C) |h - 30| < 20
D) |h - 40| < 10</p>
<p>Aren't they the same thing? The answer in the book is D, but C satisfies all height requirements as well.</p>
<p>30 < h < 50
-10 < h-40 < 10
Therefore, |h-40| < 10.</p>
<p>|h-30| < 20 implies -20 < h-30 < 20 or 10 < h < 50, which is not the same thing.</p>
<p>I see where I went wrong.</p>
<p>Thanks!</p>
<p>Plug in numbers. What if she was 11 inches tall? In reality, she wouldn’t be able to go on the ride, but according to equation C, she would be.</p>
<p>Another way to think about this problem is to recognize that 40 is the height halfway between 30 and 50. Any height, h, has to fall within 10 inches of the mid-point that is 40, this means that |h-40| has to be less than 10, or |h-40|<10.</p>