a123 Group Title 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 3 years ago 3 years ago

1. satellite73 Group Title

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

2. a123 Group Title

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

3. a123 Group Title

i keep getting x > 0

4. a123 Group Title

and x < 4/7

5. satellite73 Group Title

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. a123 Group Title

oh

7. satellite73 Group Title

$(-\infty,\infty)$

8. a123 Group Title

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

9. LagrangeSon678 Group Title

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. a123 Group Title

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. LagrangeSon678 Group Title

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