How do you solve and graph abs(n+2)>=1?

1 Answer
Dec 19, 2017

See a solution process below:

Explanation:

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.

-1 >= n + 2 >= 1

Subtract color(red)(2) from each segment of system of equations to solve for n while keeping the system balanced:

-1 - color(red)(2) >= n + 2 - color(red)(2) >= 1 - color(red)(2)

-3 >= n + 0 >= -1

-3 >= n >= -1

Or

n <= -3; n >= -1

Or, in interval notation:

(-oo, -3]; [-1, +oo)

To graph this we will draw a vertical lines at -3 and -1 on the horizontal axis.

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

We will shade to the left and right of the lines to show the intervals:

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