Couple of math questions?

Question

Can anyone tell me why | x | < p has no solution for p <= 0

and why the solution | x | > p is all real numbers for p < 0

Answer 1

If |x| < p and p <= 0, then |x| < p <=0 which means |x| < 0. But there's no number whose absolute value gives you a negative number. The absolute value of a number is always positive, with the exception of |0| = 0. So there's no solution.

Similarly, |x| >= 0 for any x. If p < 0, then 0 > p, so
|x| >= 0 > p, meaning |x| > p.

Answer 2

When you take the absolute value, you always get a + answer. Therefore the range of |x| is >0 always.

Therefore it can never be < p if p is negative (less than 0), because |x| is always > 0.

Example: |-3| < -5
3 < -5 This is FALSE.

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Same reasoning for part 2.
|x| is always > 0, so it's always going to be greater than p if P is less than 0.

Answer 3

|x| is always >= 0 by definition
so |x| < p
can only be true for p>0 and must have no solution for p<0

similarly if p<0 then it must be less than 0 or any |x|

Answer 4

because by definition |x| is the distance of x away from zero. you cannot have a negative number by that unless you say the -|x|. |x|>p if p>=0 is all real numbers b/c x is potentially any real number.

Answer 5

|x| is always positive. Therfore it cannot be negative (<0) as it would be if p were <=0.

Again, |x| is always positive. Therefore it must be greater than all p< 0 which are all negative.

Answer 6

absolute value is always positive since it represents distance from zero. |p| is never less than 0 since it can never be negative. |p| = 0 when p = 0. |p| > 0 for any non-zero number since it is always positive since it represent distance.

Answer 7

Say What?