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inequality

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2 Answers

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.
4>1/3    multiply each side by 3.   Now we have 12>3 .  Now divide both sides by 12 and we have that 1>3/12 which gives  1> 0.25   Simple not fooling around with the 1/3.

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