question about pr.10 p. 191, guide 3

[iv_stoyanov]

if 4/x < 1/3, what is the possible range of values for x?

Case I : x positive

12< x (so far so good)

Case II: x negative

in this case according to my solution, x is actually -x, so
4*3 < -x*1
12<-x /*-1
-12>x or x<-12

instead the solution is 12>x

I reviewed other problems and it is obvious that when we multiply or divide an inequality by a negative number, all numbers change signs and the inequality sign gets fliped. In the MGMAT 's solution the number 12 does not change it's sign.

I know that my question might be trivial and stupid, but am I missing an important concept here? I am really confused with this problem.

[tim]

yes, do not EVER say that because x is negative that it equals -x. just remember that it's negative when you do your calculations. in this case, that means we need to flip the inequality sign when we multiply both sides by x..

[chuperman601]

Hello, I have a question regarding Case 2 when we must consider the scenario when x is negative.

Here is how I solved Case 2: x is negative:

(4/x) < (1/3)
12< x
12 > x

So, then, my solution for the range would be:
When x is positive:
x>12

When x is negative:
x< 12

However, the solution states that the range is:
x>12 when x is positive
x<0 when x is negative.

How is x<0 arrived at?

Thank you

[jnelson0612]

Hello, I have a question regarding Case 2 when we must consider the scenario when x is negative.

Here is how I solved Case 2: x is negative:

(4/x) < (1/3)
12< x
12 > x

So, then, my solution for the range would be:
When x is positive:
x>12

When x is negative:
x< 12

However, the solution states that the range is:
x>12 when x is positive
x<0 when x is negative.

How is x<0 arrived at?

Thank you

Good question! Well, 4 divided by any negative number will yield a negative result, which will always be less than 1/3. Thus, any negative number for x will also fit the inequality.