Question

If l y + 3 l < 3, then

(A) 0 > y > -6
(B) y > 3
(C) 3 > y > 0
(D) y = -1
(E) y = -2

Mind you : the letter " l " is used for absolute value signs.

Answer 1

Answer: Choice A

Work Shown

| y+3 | < 3

-3 < y+3 < 3

-3-3 < y+3-3 < 3-3

-6 < y < 0

0 > y > -6

I'm not sure why your teacher decided to flip things when -6 < y < 0 is more standard. The rule I used on the 2nd line was |x| < k becoming -k < x < k for some positive number k. For example, |x| < 5 becomes -5 < x < 5.

The number line graph for -6 < y < 0 or 0 > y > -6 will have open circles at -6 and 0. Then we shade between those open holes. The open hole means "exclude this endpoint".