## anonymous 4 years ago Can somebody help me? I've tried to solve this problem and I just can't manage to get the right answer: |7x + 2| > -2

1. anonymous

true for all x by inspection absolute value is positive, so it is always bigger than -2

2. anonymous

how do you write it like a < x < b or something like that?

3. anonymous

i keep getting x > 0

4. anonymous

and x < 4/7

5. anonymous

it is all real numbers x can be anything. do not try to solve this using algebra. absolute value of anything is always greater than or equal to 0, so it must be always greater than -2. it doesn't matter what you put in for x, positive number or negative number

6. anonymous

oh

7. anonymous

$(-\infty,\infty)$

8. anonymous

wait, why is one of the infinity symbols negative if x is always greater than or equal to 0?

9. anonymous

what satellite means by (-inf,inf) is that you can plug any x value into the inequality, you can plug in -20000, 200, 3,4, -5, it dosent matter, you will still get a value greater than or equal to zero

10. anonymous

i still don't understand why, if you plug in a negative number, it comes out to be greater than or equal to zero

11. anonymous

beacuse of the absolute value, you see the absolute value guarantees you that the value you get out will be positive or zero, it cannot be negative