How do you write the interval [5, +infinity) as an inequality involving x and show each inequality using the real number line?

Answer 1

See a solution process below:

Because the left side of the interval is a "[" or bracket, then the inequality contains the value there which is #5# and so the inequality we right will contain an "or equal to" clause":

#x >= 5#

On the number line the left side of the line representing this interval will be a solid circle indicating the inequality contains an "or equal to" clause":

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Answer 2

Isaiah Anthony

To write the interval [5, +∞) as an inequality involving x, you use the inequality (x \geq 5). On the real number line, you represent this inequality by shading the region to the right of 5 and including 5, since it's part of the interval. There is no endpoint to the right, represented by an arrow pointing towards positive infinity.

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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.