Question

If `2/x >= 1/7` what is the largest possible value for `x`?

Answer 1

`color(green)(14)`

Explanation:

`2/14=1/7` ...so if `x=14` then `2/x = 1/7`

Note that `x` must be greater than zero for `2/x >=1/7` (otherwise `2/x` would be negative).
also if `x> 14` then `2/x < 1/7`

Answer 2

`x <= 14` , so the maximum value for `x` is 14.

Explanation:

As mentioned by Alan P., `x` has to be more than 0 ( ie positive)

It may not be equal to 0,
because it is in the denominator.
If it was negative, `2/x` could not be more than `1/7`

Now that we know that `x` is positive, there are 2 ways to solve this inequality..

• multiply both sides by `7x` to cancel the denominators

`2/cancelx xx 7cancelx >= 1/cancel7 xx cancel7x`

`14 >= x" "rarr x <= 14`

• invert both sides. (the inequality sign will change around)

`2/x >= 1/7`

`x/2 <= 7/1" "larr` multiply by 2

`x <= 14`