Question 613450
First add {{{3/2}}} to each side of the equation
{{{2/3}}}w={{{3/2}}}-{{{4/7}}}
the common denominator of {{{3/2}}} and {{{4/7}}} is 14
           so
{{{3/2}}}={{{21/14}}}and {{{4/7}}}={{{8/14}}}
          now we have
{{{2/3}}}w={{{21/14}}}-{{{8/14}}}={{{13/14}}}
             that's
{{{2/3}}}w={{{13/14}}}
    Multiply each side of the equation by{{{3/2}}}
{{{2/3}}}w x{{{3/2}}}= {{{6/6}}}w = 1w or just w
            and
{{{13/14}}}x{{{3/2}}}={{{39/28}}}
         SO
w={{{39/28}}} or 1{{{11/28}}}
We can check our answer by substituting {{{39/28}}} in the problem
{{{2/3}}} x {{{39/28}}}-{{{3/2}}} should = -{{{4/7}}}
{{{2/3}}} x {{{39/28}}}={{{78/84}}}
{{{78/84}}}-{{{3/2}}}={{{78/84}}}-{{{126/84}}}=-{{{48/84}}}
   which reduces to -{{{4/7}}}