inequality

Question

What is the solution of |x + 5| < -7

Answer 1

Given inequality |x + 5| < -7

write the inequality in form of x+5< ±7

First inequlity   form is x+5<+7

x + 5-5 < 7-5                            (Subtract each side by 5)

x<2                                         (simplify 5-5=0,7-5=2)

Second inequlity form is x+5<-7

x+5-5<-7-5                               (Subtract each side by 5)

x<-12                                      (simplify 5-5=0,-7-5=-12)

Therefore the inequality of x<-12,or x<2.

Comments

The absolute value is always positive (or zero).

Answer 2

The absolute inequality |x + 5| < -7

The absolute value is always positive (or zero).

The inequality such as |x + 5| < -7 is never true.It has no solution.

The answer is empty set ø.