Can someone pls. solve this absolute value eq? How do you solve this absolute value eq: 8|x+8| + 9 > 6?

Question

Sorry, I don't have the answer in the back of the book to reference and I would really like to know how to get the answer anyway.

Thank you if you could help me out!

Answer 1

Are you sure you copied it correctly ?

The solution seems to be "all x".

8|x+8| + 9 > 6

First subtract 9 from both sides

8 |x+8| > - 3

Simply for the sake of abbreviation,

let y = |x+8|

We have 8 y > - 3

y > -3/8

But since y is |x+8| it is  positive no matter what x is,

so the original equality is always true, for any value of x,

positive or negative, large or small.

.

Answer 2

8|x + 8| + 9 > 6

You want to isolate the absolute value.

8|x + 8| > -3

|x + 8| > -3/8

Note that, whenever we have an absolute value with a negative sign on the other side, it's either going to be always true or always false.

Since the absolute value of anything is greater than or equal to 0, then

|x + 8| > 0 > -3/8

Showing that the inequality is true for ALL real numbers.