Note I have interpreted #2x/3# as a mixed fraction; if it were intended to be a multiplication, see Solution 2 below.

**Solution 1** (#2x/3# as a mixed fraction)

If #5 < 3 - 2x/3##color(white)("XXXX")##rarr (5 < 3 - (6+x)/3)#

We can clear the fraction by multiplying everything by 3 (without effecting the validity of the inequality orientation)

#color(white)("XXXX")##15 < 9-6 -x#

Subtract 3 from both sides (again, no effect on the validity of the inequality orientation)

#color(white)("XXXX")##12 < -x#

Multiply both sides by #(-1)# (This will reverse the inequality orientation. Note that as an alternative we could have added #(x-12)# to both sides without effecting the orientation and achieve the same result)

#color(white)("XXXX")##x < -12#

**Solution 2** (#2x/3# as implied multiplication)

If #5 < 3 - 2x/3##color(white)("XXXX")##rarr (5 < 3 - 2/3x)#

Subtract 3 from both sides

#color(white)("XXXX")##2 < -2/3x#

Multiply both sides by #(-3/2)# (forcing a reversal of the inequality orientation

#color(white)("XXXX")##-3 > x#

or

#color(white)("XXXX")#x < -3#