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Negative numbers are numbers less than zero. They have a minus sign (-) in front of them. For example, -1, -2, and -3 are negative numbers.

When you negate a negative number, it becomes positive. For instance, the negation of -5 is 5.

Conversely, the negation of a positive number becomes negative. So, if you have a positive number like 3, negating it turns it into -3. Understanding this is very important in solving inequalities that involve negation.

In the given problem, recognizing how negation works helps us ascertain when - x becomes negative. If x is positive, its negation (-x) will be negative.

Inequalities are mathematical expressions showing that two values are not equal. They use symbols like < (less than) and > (greater than).

In the problem, to find for which values of x - x < 0, we created an inequality. An important thing to remember is that when you multiply or divide both sides of an inequality by a negative number, the direction of the inequality sign reverses.

For instance, if you multiply both sides of - x < 0 by -1, the inequality sign will change direction, giving you x > 0. This step is crucial for solving inequalities correctly.

Let's say we had - x > 0. By multiplying both sides by -1, this would turn into x < 0. Understanding how inequalities work helps in solving such problems effectively.

Algebra involves using symbols and letters to represent numbers and quantities in formulas and equations. It's a key part of solving math problems, including inequalities.

In the given exercise, we use basic algebra to solve the inequality - x < 0. Identifying that - x means the negation of x is an important algebraic concept.

To solve it, we applied the algebraic rule of reversing the inequality sign when multiplying or dividing by a negative number.

Algebra makes it possible to understand and manipulate expressions to find the values of variables. In this case, we found that x must be greater than 0 for - x to be negative.