Determine the Interval notation and Inequality notation of the absolute value notation: abs(x)>-5

To determine the interval notation and inequality notation of the absolute value equation "abs(x) > -5," we need to understand the concept of absolute value and how it relates to inequalities.

The absolute value of a number represents its distance from zero on the number line and is always positive. In mathematical notation, the absolute value of x is denoted as |x|.

To solve the inequality |x| > -5, we need to find the range of values for which this inequality holds true.

Since |x| is always positive, it will always be greater than any negative number. Therefore, |x| will always be greater than -5, regardless of the value of x.

In interval notation, we express this as:
(-∞, +∞), which means all real numbers.

In inequality notation, we express this as:
x ∈ (-∞, +∞), which states that x belongs to the set of all real numbers.

In conclusion, the interval notation for the absolute value inequality |x| > -5 is (-∞, +∞), and the inequality notation is x ∈ (-∞, +∞).