Question 709355
Two possiblilities to check.  One is if 3x-3>=0 and the other is for 3x-3<0.  Before going into more, factor the expression..

{{{3x-3=3(x-1)}}}.  Take care of that in the inequality statement.


4 < |3x &#8722; 3| < 5
{{{4<3abs(x-1)<5}}}
{{{4/3 < abs(x-1) < 5/3}}}


If {{{x-1>=0}}} then:
{{{4/3 < x-1 < 5/3}}}
{{{4/3+1 < x < 5/3+1}}}
{{{7/3 < x < 8/3}}}


If x-1<0 then :
{{{4/3 < 1-x < 5/3}}}
{{{4/3-1 < -x < 5/3-1}}}
{{{1/3 < -x < 2/3}}}
Now multiply all members by NEGATIVE 1 and reverse the direction of the order symbols.
{{{-1/3 > x > -2/3}}}
And to keep lesser to the left and greater to the right,
{{{-2/3 < x < -1/3}}}


FINAL RESULT STATEMENT: {{{-2/3 < x < -1/3}}} OR {{{7/3 < x < 8/3}}}