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Understanding the difference between an expression and an equation is crucial in algebra. An **expression** is a mathematical phrase that can contain numbers, variables, and operators (like + or -). However, it does not have an equal sign (=). For example, \(9r + 3(r - 4)\) is an expression. On the other hand, an **equation** is a mathematical statement that shows the equality of two expressions by using an equal sign. For instance, in the problem \(9r + 3(r - 4) = 2\), the equal sign indicates that we are comparing two expressions, making it an equation. Remember, every equation can be split into two expressions: the left-hand side (LHS) and the right-hand side (RHS), separated by the equal sign.

Spotting the equal sign is a fundamental step in distinguishing between expressions and equations. The equal sign (=) serves as a divider that separates the expressions in an equation, indicating that the values on either side are equal. In our example \(9r + 3(r-4) = 2\), the equal sign is right in the middle. If there is no equal sign, what you are looking at is simply an expression. For students starting with algebra, practicing to quickly identify the presence of an equal sign can really assist in understanding what type of mathematical statement you are dealing with. Always look for that sign during your initial scan of the problem.

A **mathematical statement** encompasses both expressions and equations. It’s a declarative sentence that can be either true or false. When dealing with mathematical statements in algebra, you are often either simplifying an expression or solving an equation. For instance, the statement \(9r + 3(r - 4) = 2\) can be solved to find the value of \(r\). As an equation, it tells us that the left-hand side and right-hand side are equal when \(r\) is found. On the other hand, an expression does not make a full statement about equality but can still be evaluated or simplified. Understanding that equations are a type of mathematical statement can help you know what actions to perform: whether to simplify, evaluate, or solve.