<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 satisfies the regulation for this ride?</p>
<p>| h-10| <50
|h-20| <40
|h-30| <20
|h-40|<10
|h-45|<5</p>
<p>Okay, what you need to do in order to visualize it, is to draw out a number line.... with "30" at the left and "50" at the right, then you can just plug in some numbers and see that c) is the correct answer</p>
<p>i just am not sure what to do with the other values.. like i pick c because i thought it would be 0< h-30<20 when the absolute values are gone.. What exactly do you do with the absolute values and i think you negative the number or something?</p>
<p>|h-40|<10 is the correct option, but it has to be solved to satisfy the question. That expression can be easily changed into -10 < h-40 < 10 and solved to result in 30 < h < 50. A simple manipulation of real numbers.</p>
<p>so to clear absolute values, just take the negated version of one of the given ranges and set it less than the x or the variable.. allright i'll try and remember that</p>
<p>i just used a value that was either less than 30 or greater than 50. For example, 29 inches.</p>
<p>C isn't the answer...it is d.</p>
<p>The way I see it, there are two ways to go about this problem. The faster way is to try to find numbers that are not between 30 and 50 that satisfy each inequality. If a number that isn't between 30 and 50 satisfies the inequality, the inequality doesn't work. If you plug in 15 for the height for c, the inequality holds true. C cannot be the correct answer. Anything you plug in that isn't between 30 and 50 for d will not satisfy the inequality. d is correct.</p>
<p>You can also do it algebraically. For d, for example, you have h-40 < 10 and h-40 > -10. Simplify both inequalities and you get h<50 and h>30. Tada! That's what we were looking for.</p>
<p>..............</p>
<p>Absolute-Value</a> Inequalities</p>
<p>is a good link</p>
<p>Oppps I did say c) didn't I?</p>
<p>Anyways, you take the equation -10<h-40<10</p>
<p>Then solve just like a linear equation: By adding 40 to both sides to cancel the -40....</p>
<p>then you will have 30<h<50</p>
<p>I just plugged 30 and 50 into the answer choices and chose the one that came out equal to the number on the right of the equation.</p>
<p>note that the expression |h-n| for a given integer n means the distance between h and n (like on a number line). Since the range is from 30 to 50, if we take the middle number 40, we note that any height for the ride must be no more than 10 units away from it. So the distance between the height and 40 on the number line must be less than 10 unites, aka |h-40| < 10.</p>