Question 756362
You simply made a sign mistake or you forgot a rule about  multiplying an inequality by a negative number.  The correct answer is {{{highlight(x<=1.867)}}}


First step is
{{{-5(x-3)>=2(4.7-x)}}} was divided by 2 on both sides.
{{{-5(x-3)-2(4.7-x)>=0}}}
And for earlier convenience a multiplication by NEGATIVE 1.
{{{5(x-3)+2(4.7-x)<=0}}} NOTICE the changed direction of the the order.


The remaining steps are omitted here knowing that you seemed to show as much skill as needed since the numeral shown in your description was correct.