SAT absolute Value problems

Test Preparation SAT Preparation
1

<p>I tend to get tripped up on these questions dealing with absolute value/inequality</p>

<li>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 the child’s height H satisfies the regulation for this ride?</li>
</ol>

<p>A l h - 10 l < 50
B l h-20 l < 40
C l h-30 l < 20
D l h - 40 l < 10
E l h - 45l < 5</p>

<p>another example of these question is on page 400 of the BB number 19.</p>

<p>Can someone share how they would go about solving these types of questions? You can plug in but an alternative method would be helpful.</p>

2

<p>You can actually do this algebraically.</p>

<p>The key thing to remember: |x|<N is the same as -N < x < N ...</p>

<p>So, we have: 30 < h < 50 but we need two numbers a and b so that |h-a| < b is the same thing.</p>

<p>Use the rule to get:</p>

<p>-b < h-a < b</p>

<p>a-b < h < b+a</p>

<p>We want: a-b = 30 and b+a = 50</p>

<p>So: a=40 and b=10 ...</p>

<p>See if you can use this for that BB problem ...</p>

3

<p>Oh wow, that helped tremendously.</p>

<p>method works fine for 2nd prob as well- you the man fignewton.</p>

4

<p>Visual approach.</p>

<p>|a-b| is the distance between the numbers a and b on the number line.</p>

<ol>
<li>The mid-point of the interval (30, 50) on the number line is 40.</li>
<li>Variable h is a pendulum positioned right above that point; initially h is 10 away from both 30 and 50.</li>
<li>h should not swing 10 or farther from 40 in either direction:
|h-40| < 10.</li>
</ol>