i am trying to solve 4/x-2>5. i use calculator and mistakenly type of digit if other than 5. when i type in the problem ,so i get the wrong solution my answer was 2<x<y. what did i mistakenly type in?

4 / x - 2 > 5

4 / x > 5 + 2

4 / x > 7 Multiply both sides with x

4 > 7 x Divide both sides with 7

4 / 7 > x

This mean:

x < 4 / 7

x must be > 0 besouse in expresion:

4 / x - 2 > 5

4 / 0 = undefined

So solution are:

0 < x < 4 / 7

For negative numbers 4 / x - 2 is always negative so negative numbers can´t be sloutions.

To solve the inequality 4/(x-2) > 5, you need to isolate the variable x. Let's go through the steps together:

1. Begin by multiplying both sides of the inequality by (x - 2) to eliminate the denominator:
4/(x-2) * (x-2) > 5 * (x-2)

Simplifying this, we get:
4 > 5(x-2)

2. Distribute 5 to (x-2):
4 > 5x - 10

3. Move the constant term to the other side of the inequality:
4 + 10 > 5x

Simplifying this further, we have:
14 > 5x

4. Divide both sides of the inequality by 5, keeping in mind to reverse the inequality when dividing by a negative number:
14/5 > x

This can also be written as:
x < 14/5

So, the correct solution is x < 14/5.

If you obtained 2 < x < y as your answer, it means you made an error while performing the calculations. I cannot determine exactly what mistake you made without the specific values you used for x and y. However, it's possible that the error could have occurred when distributing 5 to (x-2) in step 2 or during the simplification of the inequality.