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Dealing with negative numbers might seem tricky at first, but with a few basic principles, it becomes straightforward. A negative number is any number that is less than zero. We use a minus sign (-) to denote that a number is negative, such as -5 or -27.

In mathematical operations, negative numbers follow certain rules. For example:

• Adding a negative number is the same as subtracting its positive counterpart: 5 + (-3) is the same as 5 - 3.
• Subtracting a negative number turns into addition: 5 - (-3) is the same as 5 + 3.
• When multiplying or dividing two negative numbers, the result is positive: (-2) x (-3) = 6.

Keeping these rules in mind helps in effectively solving equations involving negative numbers.

Integer operations usually involve adding, subtracting, multiplying, and dividing whole numbers, both positive and negative, including zero.

When adding integers, if the signs are the same, you add the absolute values of the numbers and keep the common sign. For example, adding (-3) + (-5) gives -8 because both integers are negative.

Conversely, if the signs are different, subtract their absolute values and use the sign of the integer with the larger absolute value. So, for 7 + (-10), the answer is -3, since the absolute value of -10 is larger, and thus the result takes the negative sign.

Multiplying and dividing integers involve remembering that a negative times or divided by a positive always yields a negative result. Conversely, two negatives yield a positive result when multiplied or divided.

In basic algebra, we often work with simple equations and expressions using variables and constants. Constants are specific numbers, while variables represent unknown values and are usually denoted by letters such as \(x\) or \(y\).

Algebraic operations follow the standard order of operations: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right) - often remembered by the acronym PEMDAS.

In algebra, like absolute value problems, understanding substitution is key. For instance, when \(|x|\) is given, it means finding the distance from zero on the number line, regardless of direction, leading it to always be non-negative.

These foundational concepts are used extensively not only in solving equations but also in real-world applications, making algebra a vital part of mathematics.