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How do you graph and solve #|x| ≥ 2 #?

Answer 1

See a solution process below:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

#-2 >= x >= 2#

#x <= -2# and #x >= 2#

To graph this we will draw vertical lines at #-2# and #2# on the horizontal axis.

The lines will be solid lines because the both inequality operators contains an "or equal to" clause.

We will shade to the left and right side of the line because the inequality operator contains a "less than" and "greater than" clause respectively:

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Answer 2

Ethan Adkins

To graph and solve the inequality ( |x| \geq 2 ), first, draw a number line. Mark the points -2 and 2 on the number line. Then, shade the region to the left of -2 and to the right of 2, including the endpoints. This represents the solution set of the inequality.

The solution to the inequality ( |x| \geq 2 ) is ( x \leq -2 ) or ( x \geq 2 ).

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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.