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#

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.)

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Answer 2

The interval ((1, 2)) can be written as the inequality (1 < x < 2). To represent this inequality on a real number line, you would draw an open circle at 1 and another open circle at 2, then draw a line connecting them to indicate that all values of (x) between 1 and 2 (excluding 1 and 2) satisfy the inequality.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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