How do you solve and graph #abs(w-2)<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 < w - 2 < 2#

#-2 + color(red)(2) < w - 2 + color(red)(2) < 2 + color(red)(2)#

#0 < w - 0 < 4#

#0 < w < 4#

Or

#x > 0# and #w < 4#

Or, in interval notation:

#(0, 4)#

To graph this we will draw two vertical lines at #0# and #4# on the horizontal axis.

The line will be a dashed lines because the inequality operators do not contain an "or equal to" clause.

We will shade between the two lines to capture the interval solution:

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Answer 2

To solve and graph the inequality |w - 2| < 2, you first isolate the absolute value expression and set up two cases:

  1. Case: (w - 2 < 2)
  2. Case: (w - 2 > -2)

Solve each case separately, then graph the solution set on a number line. The solution will be the intersection of the two separate solution sets from each case.

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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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