91Ó°ÊÓ

Inequalities are mathematical expressions used to compare the sizes of two values. An inequality tells us whether one value is smaller, larger, or sometimes even equal to another value. They are represented using different symbols that can help us understand relationships between numbers:

• ">" means greater than.
• "< " means less than.
• "\( \geq \)" means greater than or equal to.
• "\( \leq \)" means less than or equal to.

Inequalities are crucial in evaluating real-world scenarios, like deciding if a budget is exceeded or if a person has enough of something. They give us the flexibility not just to compare, but also to understand how much one quantity is in relation to another. Knowing how to interpret these inequalities allows us to solve problems quickly and accurately.

Negative numbers are numbers that appear on the left side of zero on a number line. These numbers are less than zero and are important when representing things like debt, temperature below freezing, and other concepts where values drop below a defined zero point. When compared with positive numbers, negative numbers will always be less.
To visualize this, imagine a thermometer: if it reads -13°C, that's much colder than 0°C. In mathematical terms, -13 is much less than 0. An easy way to recognize negative numbers is by the minus sign they carry, which acts as an indicator of their direction away from positive values.
When evaluating inequalities involving negative numbers, it’s helpful to use a number line. By observing positions on the number line, you can easily determine which of the numbers is greater or smaller.

The mathematical expression "greater than or equal to" is signified by the symbol \( \geq \). It's a versatile tool in math that shows us whether one number is larger than or at least equal to another number. For example, when asked if 0 is \( \geq \) -13, we're checking if 0 is either greater or equal.
In practical terms, this is like saying, "0 is either bigger than -13 or the same value as -13." It's a useful way of handling inequalities because it includes both possibilities—greater or equal—into one statement.
On the number line, 0 stands to the right of -13, demonstrating clearly that 0 is indeed greater, which makes our inequality \( 0 \geq -13 \) hold true. This dual condition helps in a wide array of mathematical and real-life situations, streamlining problem-solving where equal components must also be considered.