SOLUTION: Help to solve steps of the inequality... (x+1)/(x-3)<5 I actually know that the answer is 3<X<4 but other than looking at it, I don't know the steps that are used to get this answ

Question 518534: Help to solve steps of the inequality... (x+1)/(x-3)<5 I actually know that the answer is 3
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
(x+1)/(x-3) < 5
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x cannot be 3 as the left side of the inequality would be undefined.
Solve the EQUALITY: x+1 = 5x-15 ; 4x = 16 ; x = 4
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Draw a Number line; plot x = 3 and x = 4 on the line.
Test a value in each of the three line intervals to
find the solution intervals.
--------------------
If x = 0 you get (0+1)/(0-3) <5 ;
true so solutions in the interval (-oo,3)
===================================
If x = 3.5 you get (3.5+1)/(3.5-3)<5 ; false
===================================
If x = 5 you get (5+1)/(5-3) < 5 ; true so solutions in (4,+oo)
==========================================
Solution: (-oo,3)U(4,+oo)
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Cheers,
Stan H.
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Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
(x+1)/(x-3)<5
x+1<5x-15
-4x<-16
divide by -4 and reverse inequality sign
x>4
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