How do you solve #abs(3+d)< -4#?

1 Answer
smendyka
May 3, 2017

See the solution process below:

Explanation:

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.

#4 < 3 + d < -4#

Subtract #color(red)(3)# from each segment of the system of equations to solve for #d# while keeping the system balanced:

#-color(red)(3) + 4 < -color(red)(3) + 3 + d < -color(red)(3) - 4#

#1 < 0 + d < -7#

#1 < d < -7#

Or

#d < -7# and #d > 1#

Or, in interval notation:

#(-oo, -7)# and #(1, oo)#

Related questions
See all questions in Absolute Value Inequalities
Impact of this question
1144 views around the world
You can reuse this answer
Creative Commons License