# Which of the following expressions correctly determines that x is greater than 5 and less than 10?

## Question: Which of the following expressions correctly determines that x is greater than 5 and less than 10?

## (a) x < 5 & x < 10 (b) 5 < x < 10 (c) 10 < x < 5

When one expression is greater than or less than another expression, we have inequality.

## Answer: option (b) correctly determines that x is greater than 5 and less than 10?

The given expressions are the inequalities. Let's see what does each inequality means.

## Explanation:

(a) x < 10 & x < 20 means that x is less than 5 and x is less than 10.

(b) 10 < x < 20 means all the values of x between 5 and 10. This means values of x greater than 5 and less than 10.

(c) 10 < x < 5 means all the values of x between 10 and 5. This means values of x greater than 10 and less than 5. Such values of x do not exist.

### So, the correct option is (b).

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