Home > Algebra > Absolute Value Inequalities

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

Answer 1

See the solution process below:

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#

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

Or, in interval notation:

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

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Savannah Anderson

The absolute value of any real number is always non-negative. Therefore, the absolute value of any expression cannot be less than a negative number. Thus, there are no solutions to the inequality (|3 + d| < -4).

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve #abs(3+d)&lt; -4#?

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