Question

How do you write the interval (1, 2) as an inequality involving x and show each inequality using the real number line?

Answer 1

`1 < x < 2`

Explanation:

When writing intervals as inequalities we need to remember that parentheses, like, `(a,b)` are equivalent to strict inequalities, so `(a,b) rarr a < x < b`. Brackets, like `[a,b]` are equivalent to inclusive inequalities, so `[a,b] rarr a <= x <= b`.

For this problem `(1,2) rarr 1 < x < 2`.

On a number line put 1 and 2.
Put open circles at 1 and at 2.
Shade the region of between the circles.
(Not sure how to conveniently show that on here.)