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                

Solution:

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

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

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

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

So, the correct option is (b).

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

Summary:

Option (b) correctly determines that x is greater than 5 and less than 10