Note that your inequality
4 > (1/3) j
is equivalent to
(1/3) j <4
(Do you see why?)
If we multiply both sides of the inequality by 3, then we get
3*(1/3) j < 3*4
or
j < 12
Note that if we had multiplied or divided by a negative, then we would have to flip the inequality sign.
In regard to your solution. The idea was correct, namely divide both sides by 1/3. The problem occurred when you divided 4 by 1/3:
4/(1/3)
Since 4=4/1, we can rewrite the above as
(4/1) / (1/3).
To divide fractions, we flip the denominator and multiply:
4/1 * 3/1 = 12/1 = 12,
the desired result.
11/24/2013

Jonathan G.