Sage-Tips

Why is absolute value of x equal to X?

Meaning, that unless x has a value of 0, the Absolute value of x is ALWAYS positive… |x| = |x| Because Absolute value depicts only the distance from 0, not direction, and there is no way to graphically depict a number stripped of it’s +/-.

What does X mean in absolute value?

modulus
The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. The absolute value of a number may be thought of as its distance from zero along real number line.

Can X in an absolute value be negative?

Definition and properties The absolute value of x is thus always either positive or zero, but never negative: when x itself is negative (x < 0), then its absolute value is necessarily positive (|x| = −x > 0).

Why does the absolute value of x have no solution?

For example, |x|=−1 has no solution. The absolute value of a number is its distance away from zero. That number will always be positive, as you cannot be negative two feet away from something. So any absolute value equation set equal to a negative number is no solution, regardless of what that number is.

Does absolute value make everything positive?

No. Absolute value is always positive. Since it’s the distance a number is from 0, it would always be positive.

What is the absolute value of |- 9?

9
The absolute value of −9 is 9.

Is absolute value is always positive?

Absolute value is always positive. Since it’s the distance a number is from 0, it would always be positive. So, the absolute value of positive 5, would be positive 5.

What is the absolute value of -|- 12?

The absolute value is the distance between a number and zero. The distance between −12 and 0 is 12 .

What is the absolute value of X when x is zero?

Which says the absolute value of x equals: x when x is greater than zero. 0 when x equals 0. −x when x is less than zero (this “flips” the number back to positive) So when a number is positive or zero we leave it alone, when it is negative we change it to positive using −x.

Is there a number with an absolute value that is negative?

\\left| x ight| =\\, – 5 ∣x∣ = −5 . The absolute value of any number is either positive or zero. But this equation suggests that there is a number that its absolute value is negative.

How do you find the absolute value of a given equation?

So, this leads to the following general formula for equations involving absolute value. If |p| = b, b > 0 then p = −b or p =b If | p | = b, b > 0 then p = − b or p = b. Notice that this does require the b b be a positive number. We will deal with what happens if b b is zero or negative in a bit.

Is the expression inside the absolute value symbol a single variable?

This problem is getting interesting since the expression inside the absolute value symbol is no longer just a single variable. Don’t worry; the set-up remains the same. Just be careful when you break up the given absolute value equation into two simpler linear equations, then proceed how you usually solve equations.