How do you solve #5< 3- 2x/3#?

1 Answer
Jul 16, 2015

Answer:

#x < -12 or x < -3#
#color(white)("XXXX")#depending upon interpretation of #2x/3#

Explanation:

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#