Question

help asap !
| y + 4 | < 1

Answer 1

Are you graphing, plotting, or interval notation?

Answer 2

none, just solving

Answer 3

Okay. Well do you know your first step?

Answer 4

i know the first step, i just need help w/ picking the answer. I did 1 minus -4 and my answer was -3. i just need to know why two of my answer choices are saying -3 < y < 5
and 5 < y < -3.

Answer 5

What I usually do is plug in a number that satisfies the first answer choice into my original problem. Then, I do this with a number that satisfies my second answer choice.

For example, first plug in 4 and check
Then, plug in 6 and -2 and check.

Answer 6

Don't take this the wrong way, but you don't know the first step.
I'll explain it to you.
An absolute value inequality with a \(\lt\) sign needs to be solved in a very specific way.

Answer 7

To solve the absolute value inequality

\(|X| \lt k\), where X is an expression containing a variable, and k is a non-negative number

solve the compound inequality

\(-k \lt X \lt k\)

Answer 8

Now let's look at your case.

Solve the absolute value inequality:
| y + 4 | < 1

In this case, we see that y + 4 is the expression with a variable, and k is 4.
We use the rule above and we change the absolute value inequality into the following compound inequality:

\(-1 \lt y + 4 \lt 1\)

Now we subtract 4 from all three sides:

\(-5 \lt y \lt -3\)

Answer 9

Do you see how it works?

Answer 10

ooh, yeah i see now. my friend explained it to me differently and she made it seem complicated.

Answer 11

thank you !

Answer 12

This method is for absolute value inequalities with < or <=.
If an absolute value inequality uses > or >=, then it's different.
You need to use two inequalities separated by "or", not by "and."