<p>If 2x-5, x+1 and 3x-8 are all integers and x+1 is the median of these integers, which of the following could be a value for x? </p>
<p>5
7
9
10
11</p>
<p>Plugging in doesn't take long- Is there another way to go about solving these problems?</p>
<p>Plugging it in is still probably faster, but you could solve it algebraically.</p>
<p>Just set x+1 = 2x-5 and x+1 = 3x-8.</p>
<p>Solving those equations gives you x = 6 and x = 4.5. The answer has to be between those values.</p>
<p>Oh thats clever. I get it, thanks.</p>
<p>This problem is one where plugging in is probably best, but I suppose if you are fast with your graphing calculator, you could plot three lines, e.g. y=2x-5 etc. and check when y=x+1 is between the others...</p>
<p>You can just solve those equations in your head in a few seconds. It actually depends on how many ties it takes you with the plugging in part. If you happen to shoose the right one on the first try, then plugging in will be faster. But if its takes u 3-5 tries, then simply solving it may have saved some time. It doesn't matter really. Its just the difference between napping for 5 mins at the end of the section and napping for like 5.1 minutes.</p>
<p>(5x-13)/2=x+1-->5x-13=2x+2-->3x=15-->x=5</p>
<p>Sorry but median does not equal mode. That may work with this set of numbers, but that is a bad practice to get into.</p>
<p>See, median is the middle value out of a set of values arranged in the increasing order.
So you should have :
2x - 5 < = x+1
AND
x + 1 < = 3x-8</p>
<p>That's the proper method mathematically.</p>
<p>Once again, that will not always work. You cannot assume that 2x-5 is the smallest and that 3x-8 is the largest. It happens to be so in this problem, but it may not always be so. Median is the middle, but you don't know which ones are on the ends. So you might as well set it to = instead of <= or >=. You know that x will be between the two answers, so no need to confuse yourself with greater than and less than signs.</p>