Solve the inequality and specify any excluded values? #-2 < (3x+1)/(x-3)#

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Answer 1 · 2017-02-28T19:03:57

#x>1, x!=3#

First, keep in mind that you need

#x - 3 !=0 implies x !=3#

since #x=3# would make the denominator equal to #0#.

Now, multiply both sides by #x-3# to get

#-2(x-3) < 3x+1#

Next, expand the brackets

#-2x+6<3x+1#

Don't forget your rules for multiplying negatives!

Next, do some rearranging to get the #x#'s on one side and the other terms on the other side

#6 < 5x+1#

#5 < 5x#

Therefore,

#1 < x " "# or #" "x > 1#

I hope this helps.