# How do you solve and graph #abs(x-2)<=3#?

See a solution process below:

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

The solution is:

Or, in interval notation form:

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To solve and graph ( |x - 2| \leq 3 ), follow these steps:

- Break it into two cases: ( x - 2 \geq 0 ) and ( x - 2 < 0 ).
- For ( x - 2 \geq 0 ), solve ( x - 2 \leq 3 ) for ( x ).
- For ( x - 2 < 0 ), solve ( -(x - 2) \leq 3 ) for ( x ).
- Plot the solutions on a number line.
- Shade the region where the solutions lie, including the boundary points.

This will give you the graph of the inequality ( |x - 2| \leq 3 ) on the number line.

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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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