Question 30617
{{{ -3<(3x-1)/5<1/2 }}} and {{{ 1/3<(3-2x)/6<9/2 }}}
We will solve these one at a time.  As these are compound inequalities, like an equation where if you add 5 to each side .... here you do it to all three parts of the inequality.
{{{ -3<(3x-1)/5<1/2 }}} Multiply by 5
{{{ -15<3x-1<5/2 }}} Add 1
{{{ -14<3x<7/2 }}} divide by 3
{{{ -14/3<x<7/6 }}}  the smaller value is on the left, the larger on the right, and the <> symbols are pointing left.  If you need to reduce the fractions to mixed numbers, do so now.
{{{ 1/3<(3-2x)/6<9/2 }}} Multiply by 6
{{{ 6/3<3-2x<54/2 }}} reduce the fractions now
{{{ 2<3-2x<27 }}} subtract 3
{{{ -1<-2x<24 }}} Divide by negative 2 
DONT FORGET TO FLIP THE < > SYMBOL WHEN * OR / BY A NEGATIVE!!!!
{{{ 1/2>x>-12 }}} Smaller number needs to be on the left ... flip the WHOLE thing end for end
{{{ -12<x<1/2 }}}