Sage-Tips

Why does the absolute value of x 0 have no solution?

An absolute value is the distance of a number from zero on the number line. In this case, we have the absolute value of x is less than 0. Because of the definition of absolute value, the absolute value of x cannot be negative; it must be positive. Therefore, the absolute value cannot be less than 0.

What is the absolute value of X if X 0?

if x < 0, then |x| = −x. That is, if x is non-negative: |3|, then the absolute value is the number itself. If x is negative: |−3|, then the absolute value is its negative; that makes the absolute value positive.

What do you do when an absolute value equation equals zero?

In the case of only one solution, you end up with an absolute value expression equal to zero. Since this means that the distance from zero on the number line is zero, you end up with only one equation.

Does the absolute value of x equal X?

More Formal. Which says the absolute value of x equals: x when x is greater than zero.

Is it possible for an absolute value equation to have no solution one solution if so what would each look like graphically?

Yes; yes; A graph with the horizontal line entirely below an upward-opening absolute value function, or above a downward-opening absolute value function, will not have points of intersection and the equation will have no solutions.

How do you know if an absolute value has no solution?

Recall that an absolute value expression can never be less than zero. That is, a fully reduced absolute value expression must be greater than or equal to zero. If you’ve simplified an absolute value equation and the value on the other side of the equals sign is a negative number, the equation has no solution.

What’s the absolute value of 0?

0
The absolute value of 0 is 0. (This is why we don’t say that the absolute value of a number is positive. Zero is neither negative nor positive.)

Why does absolute value have two solutions?

And represents the distance between a and 0 on a number line. Has two solutions x = a and x = -a because both numbers are at the distance a from 0. You can write an absolute value inequality as a compound inequality. …

Can an absolute value equal zero?

Does zero have an absolute value?

The absolute value of 0 is 0. (This is why we don’t say that the absolute value of a number is positive. Zero is neither negative nor positive.)

What is the absolute value of the absolute value of x?

The absolute value (or modulus) | x | of a real number x is the non-negative value of x without regard to its sign. For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5. The absolute value of a number may be thought of as its distance from zero along real number line.

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 the absolute value always a positive number?

Therefore, the absolute value is always a positive value and not a negative number. If the number is positive then it will result in a positive number only. And if the number is negative, then the modulus of this number will also be a positive number.

What is the equation for an absolute value function?

More generally, the form of the equation for an absolute value function is y = a | x − h | + k. Also: The vertex of the graph is ( h, k). The domain of the graph is set of all real numbers and the range is y ≥ k when a > 0.

Which graph shows the absolute value of a number?

The graph of absolute values is called the absolute value graph. As we know the absolute value of any real number is positive, so the absolute value of any number or function graph will lie on the positive side only. Example: Graph the absolute value of the number -9. Solution: Absolute value of |-9| is +9.