Question 599314
{{{-7(11-4w)-15w=-27-(50-13w)}}} Start with the given equation.



{{{-77+28w-15w=-27-50+13w}}} Distribute.



{{{13w-77=-27-50+13w}}} Combine like terms on the left side.



{{{13w-77=13w-77}}} Combine like terms on the right side.



{{{13w=13w-77+77}}} Add {{{77}}} to both sides.



{{{13w-13w=-77+77}}} Subtract {{{13w}}} from both sides.



{{{0w=-77+77}}} Combine like terms on the left side.



{{{0w=0}}} Combine like terms on the right side.



{{{0=0}}} Simplify.



Since this equation is <font size=4><b>always</b></font> true for any w value, this means w can equal any number. 


So there are an infinite number of solutions.