How do you solve #|r + 3| ≥ 7 #?

1 Answer
Mar 25, 2018

Answer:

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.

#-7 >= r + 3 >= 7#

Now, subtract #color(red)(3)# from each side of the system of inequalities to solve for #r# while keeping the equation balanced:

#-7 - color(red)(3) >= r + 3 - color(red)(3) >= 7 - color(red)(3)#

#-10 >= r + 0 >= 4#

#-10 >= r >= 4#

Or

#r <= -10#; #r >= 4#

Or, in interval notation:

#(-oo, -10]#; #[4, +oo)#