help again simplifying -5(x-1)< 5(x+1)

my text keeps getting cut off plz ignore this threas unless i verify i submitted my full question
 
i cannot seem to use the inequality symbol in my posts due to technical error. i will substitute by writing it out in regular english. so my problem once again is..-5(x-1) is less than 5(x+1)multiply each side by 1/5...(1-x) is less than (x+1)but why i ask does the (x-1) on the left side of the inequality become (1-x) ???
 
i cannot seem to use the inequality symbol in my posts due to technical error. i will substitute by writing it out in regular english. so my problem once again is..-5(x-1) is less than 5(x+1)multiply each side by 1/5...(1-x) is less than (x+1)but why i ask does the (x-1) on the left side of the inequality become (1-x) ???

5(x1)<5(x+1)\displaystyle \displaystyle{-5(x-1) < 5(x+1)}

Multiplied through by 15\displaystyle \displaystyle{\frac15}

yields:

(x1)<(x+1)\displaystyle \displaystyle{-(x-1) < (x+1)}

(In your original post there is the negative sign missing!)

x+1<x+1      x>0\displaystyle \displaystyle{-x+1 < x+1~\implies~x > 0}
 
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