Intervals to Solve Rational Inequalities

J

JSmith

Junior Member
Joined
Sep 21, 2012
Messages
120
State the intervals that must be considered in the process of solving (1-x)/(x-5) > (2-x)/(x+6).

The intervals would be the vertical asymptotes and points of intersection would they not???
 
Well, the intervals are the regions between such points. The intervals also include the two intervals from negative infinity to the lowest zero or asyptote and from the largest zero or asymptote to infinity.
 
JSmith said:
State the intervals that must be considered in the process of solving (1-x)/(x-5) > (2-x)/(x+6).

The intervals would be the vertical asymptotes and points of intersection would they not???
Click to expand...

Using graphing calculator, plot both the functions and pontificate.....
 
My "process of solution" differs from yours.

Were I to work this exercise, I would use the asymptotes and x-intercept from the following simplification to define the requested intervals. :cool:

(3x-4)/[(x-5)(x+6)] < 0
 
mmm4444bot said:
My "process of solution" differs from yours.

Were I to work this exercise, I would use the asymptotes and x-intercept from the following simplification to define the requested intervals. :cool:

(3x-4)/[(x-5)(x+6)] < 0
Click to expand...

Thanks!

Can you show me how you simplified to that, I am getting a different answer.
 
I subtracted (2-x)/(x+6) from both sides.

I combined the resulting expression on the left-hand side into a single ratio.

There must have been a multiplication of both sides by some negative value, at the end, as I see that the direction of the inequality symbol reversed.

If you need more help on the simplication, please post your results. :cool:
 
Hi. The first line above does not match the inequality in your original post.

Is the first line above correct, and you made a typographical error in your original post OR is it the other way around?

JSmith said:
State the intervals that must be considered in the process of solving (1-x)/(x-5) > (2-x)/(x+6).

Click to expand...
 
My apologies, I definitely made a typo in the original post. It is in fact (x+5), not (x-5)
 
Looks good, except for the very last line.

When you multiply (or divide) both sides of an inequality by a negative number, then you must reverse the direction of the inequality symbol.

(x+2)/[(x+5)(x+6)] < 0


PS: If you continue putting in the extra effort to format your math expressions, please place a blank line between your equations/inequalities, for ease of reading. Cheers. :cool:
 
You must log in or register to reply here.
Top