SOLUTION: Solve for x: 2x+1 <3 _____ x-5 I tried this: x and x cancel eachother so its x+1 <3 ___ -5 then multiply the demonator and numerator by 5/1 so that leaves

SOLUTION: Solve for x: 2x+1 <3 ___ x-5 I tried this: x and x cancel eachother so its x+1 <3 _ -5 then multiply the demonator and numerator by 5/1 so that leaves

Question 220734: Solve for x:
2x+1 <3
_____
x-5
I tried this:
x and x cancel eachother so its
x+1 <3
___
-5
then multiply the demonator and numerator by 5/1 so that leaves x<3???
Found 2 solutions by tutor_paul, stanbon:
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!

Whoa there... you can't cancel the x's in this case...you can only cancel factors, not when x is added to something.
In this case, first multipy each side of the inequality by (x-5):

Now you can cancel the x-5 terms on the left because they are factors. This leaves you with:

Now multipy out the term on the right:

Next you want to get the x terms on one side of the inequality and other terms on the other side.
Add -3x to both sides:

Simplify:

Add -1 to each side:

Simplify:

Multiply each side by -1. Note, when you multiply each side by a negative number, you must swap the inequality:

==============
Good Luck,
tutor_paul@yahoo.com

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve for x:
2x+1 <3
_____
x-5
======================
(2x+1)/(x-5) < 3
---------
You can see that x cannot be 5
----------------
Draw a Number line and mark x = 5
-------------------
Now check a value from each of the resulting intervals
in the inequality to see where the solution set lies.
----------------------
Check x = 0; you get: (1/1)<3 ; true, so solutions in (-inf,5)
----------------------
Checx x = 10; you get: 21/5 < 3 ; false so no solutions in (5,+inf)
-------------------------------
Let's see what it looks like:
I'll graph the left side and the right side separately:

===================================
Cheers,
Stan H.
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