Home > Algebra > Absolute Value Inequalities

How do you solve #abs(6x+5)<-1#?

Answer 1

There is no solution.

Consider what the absolute value function #|x|# actually does. Regardless of the sign of #x#, #|x|# is always greater than or equal to 0.

Now, the inequality wants us to find all values of #x# such that #|6x + 5| < -1#, but #|6x + 5| >= 0# for all #x#.

There is no solution.

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

Answer 2

Hazel Anglin

The absolute value of a number cannot be less than a negative number. Therefore, the inequality abs(6x + 5) < -1 has no solution.

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(6x+5)&lt;-1#?

How do you solve #abs(6x+5)<-1#?