Question

How do you solve |y+9|>4?

Answer 1

Absolute value means that it doesn't matter if the number in the bars is positive or negative, it still comes out to be a positive number. Since the absolute value of anything greater than -4 added with 9 is greater than 4, one answer is y>-4. Absolute value inequalities and equation often have two answers though, a positive and a negative. And since the absolute value of anything less than -14 plus 9 is greater than 4, the second answer is y<14.

Answer 2

This is a weird one.  I'm going to work it, but I also want you to look back at the
book or the worksheet and make sure that you copied it correctly.
Because it's weird, I tell you.

| y + 9 | > 4

Subtract 9 from each side of the inequality:

   | y | > -5

OK.  Now, here we go:

'Absolute value' means just the size of the number, no matter whether it's
negative or positive.  So the absolute value of every number is positive.

Got that ?  The absolute value of every number is positive.

So EVERY number is a solution to this inequality.  It doesn't matter what number
' y ' is, its absolute value is always positive.  And if the absolute value is always
positive, then it's definitely always greater than -5 .

Weird ?  I told you so.