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How do you solve #-abs(5/3y+4)>2/5#?

Answer 1

Genesis Allen

The answer is #x in (-oo;-2 16/25) uu (-2 4/25;+oo)#

First you have to simplify the absolute value. To do this you use the identity

#|x|>a iff (x<-a vv x>a )# So you get a set of linear inequalities

#5/3 y +4 > 2/5 vv 5/3 y +4 < - 2/5#

To simplify the inequalities you can multiply both sides by 15 to get rid of the fractions.

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Answer 2

Jace Anderson

To solve the inequality -|5/3y + 4| > 2/5:

Start by isolating the absolute value expression by dividing both sides of the inequality by -1, which reverses the inequality sign: |5/3y + 4| < -2/5
Since the absolute value cannot be negative, this inequality has no solution.

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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(5/3y+4)&gt;2/5#?

How do you solve #-abs(5/3y+4)>2/5#?