Question

solve absolute value of |(3x+1)/(x-1)| < 2

Answer 1

\[|(3(x+2/3 -5/3 +5/3))/(x-1)|<2\]pulled out 3 then +'s and -'s 5/3

\[|(3(x-1 +5/3))/(x-1)|<2\]
\[|3(x-1)/(x-1) +3(5/3)/(x-1)|<2\]
\[|3 +5/(x-1)|<2\]
\[-2<3 +5/(x-1)<2\]
\[-5<5/(x-1)<-1\]
\[-1/5>(x-1)/5>-1 \]
\[-1>x-1>-5 \]
\[0>x>-4 \]