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Simplifying expressions is a fundamental concept in prealgebra. It involves rewriting an expression or equation in its simplest form. This often requires performing operations like addition, subtraction, multiplication, and division, and may include handling fractions or decimals. In essence, you're trying to make the expression as short and straightforward as possible.

An essential step is to remove any parentheses—typically done by distributively multiplying each term inside the parentheses by the term outside. In our example, the expression \(0.05x + 0.02(4-x)\) involves distributing the 0.02 across the terms inside the parentheses. As a result, you expand to form \(0.05x + 0.08 - 0.02x\).


Simplification doesn't change the value of the expression but makes it easier to read and work with. This process lays the foundation for solving more complex algebraic problems as it helps develop a systematic approach to manipulating mathematical statements.

After expanding expressions, the next fundamental task is combining like terms. Like terms have the same variable parts raised to the same power. To combine them, you add or subtract the coefficients (the numerical parts) of these terms.

• In the expression \(0.05x + 0.08 - 0.02x\), the like terms are \(0.05x\) and \(-0.02x\), since they both contain the variable \(x\).
• Combining them requires performing the subtraction \(0.05 - 0.02\) to get \(0.03x\).

This simplification reduces clutter in the expression and reveals the underlying mathematical relationships more clearly. By effectively combining like terms, the expression becomes simpler and thus, more manageable.

Algebra introduces us to the use of symbols and letters to represent numbers. Basic algebra is where you start to manipulate these symbols to perform operations. You will encounter terms, coefficients, and constants, among others.

• Understanding variables is key; variables stand for unknown values and can change.
• Coefficients are the numbers in front of variables, telling how many of that variable we have.

In the expression we've worked with, \(x\) is the variable, \(0.05\) and \(-0.02\) are coefficients, while \(0.08\) is a constant—a number without a variable.

Algebra is like learning a new language of mathematics where simplifying and restructuring math problems becomes critical. It prepares you to solve equations and inequalities, paving the way for higher-level math courses. Understanding these basic concepts thoroughly is pivotal for success in math studies.