heshamelaziry wrote:If i have 1/5 < 1/k-1 < 1/2

How do we say that k-1 = 3 or 4 ??????

I see k-1 is less than 2 and more than 5, because on the number line k-1 is more than 5 and less than 2.
I am getting the opposite of the OE.

Let us do 1/(1/5), 1/(1/k-1) and 1/(1/2).

When we do these operations the comparison signs will reverse. For example : 4>3 But 1/4 < 1/3

So we have
5 > k-1 > 2

know we can see that k =5, 4.

Because you are looking at the denominator, you actually have to switch the inequality signs.

For example: 1/5 < 1/2 but 5>2. When you take the inverse, the order switches.

For our original problem

1/5 < 1/k-1 < 1/2

means 5 > k-1 > 2, so 6>k>3.

Notice the fractions were flipped, as well as the direction of the inequality. Then you just solve for k.

grockit_jake wrote:Because you are looking at the denominator, you actually have to switch the inequality signs.

For example: 1/5 < 1/2 but 5>2. When you take the inverse, the order switches.

For our original problem

1/5 < 1/k-1 < 1/2

means 5 > k-1 > 2, so 6>k>3.

Notice the fractions were flipped, as well as the direction of the inequality. Then you just solve for k.

i guess the options in the answers will help make that assumption.