inequality

Question

4>1/3j

 

I started out like this

 

j divided by 1/3 and 4 divided by 1/3 equal j<1.33333...

 

I'm not sure if this is the correct way to solve this problem?

Answer 1

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.

Answer 2

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.