How do you solve and graph #abs(x-3)>=1#?

1 Answer
Jul 31, 2017

Answer:

See a solution process below:

Explanation:

The absolute value function takes any negative or positive 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 >= x - 3 >= 1#

Add #color(red)(3)# to each segment of the system of inequalities to solve for #x# while keeping the system balanced:

#-1 + color(red)(3) >= x - 3 + color(red)(3) >= 1 + color(red)(3)#

#2 >= x - 0 >= 4#

#2 >= x >= 4#

Or

#x <= 2# and #x >= 4#

Or, in interval notation:

#(-oo, 2]# and #[4, +oo)#

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