Question 855591
First just translate the statement.


{{{2-3x<5(2-x)<=3(2-x)+10}}}


Do the multiplications.
{{{2-3x<10-5x<=6-3x+10}}}
{{{2-3x<10-5x<=16-3x}}}
A sensible step may be add 3x to each member, to result in:
{{{2<10-2x<=16}}}, which seems to be a very well chosen step.
coninue:
{{{2-10<10-2x-10<=16-10}}}
{{{-8<-2x<=4}}}
CAREFUL, DIVIDING BY NEGATIVE TWO,...
{{{highlight(4>x>=-2)}}}




Dividing by a negative value must reverse the direction of the inequality symbols.