How do you solve and graph #abs(r+1)<=2#?

1 Answer
Jan 28, 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. We can rewrite this problem as:

#-2 <= r + 1 <= 2#

Subtract #color(red)(1)# from each segment of the system of inequalities to solve for #r# while keeping the system balanced:

#-2 - color(red)(1) <= r + 1 - color(red)(1) <= 2 - color(red)(1)#

#-3 <= r + 0 <= 1#

#-3 <= r <= 1#

Or

#r >= -3#; #r <= 1#

Or, in interval notation

#[-3, 1]#

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

The lines will both be solid lines because their inequality operators both contain an "or equal to" clause. This indicates both #-3# and #1# are part of the solution set.

We will shade to the regional between the lines to show the solution set:

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