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Before diving into algebraic expressions, it's essential to understand what verbal expressions are. Verbal expressions are phrases we use in everyday language that describe mathematical ideas. For example, saying "the sum of" indicates addition. If you hear someone say "the sum of 2x, 7x, and 4," they mean to add these numbers together.
In translating verbal expressions to mathematical expressions, words like "sum," "product," "less," and "more" are crucial. Recognizing these words helps you decide the mathematical operation needed. In our example, knowing "the sum of" made it clear we needed to add the numbers together.
Once you understand the verbal cues, you can easily transition them into algebraic expressions by writing each component in a mathematical form. This step bridges everyday language and the precise language of mathematics.

When you move from the verbal to the algebraic expression, a powerful tool is combining like terms. So, what are like terms? These are terms in an expression that have the same variable raised to the same power. They can be combined by performing the operations specified.
In the expression from our exercise, we had two terms that included the variable 'x': the terms were \(2x\) and \(7x\). Both are like terms because they have the same variable 'x' and the same power (in this case, power 1, but it is typically not shown).
By adding \(2x\) and \(7x\), you simplify the expression to \(9x\). This process makes expressions easier to work with and understand. It's much more simple to handle \(9x + 4\) rather than seeing each piece separately as \(2x + 7x + 4\).

After writing the initial algebraic expression and combining like terms, the next goal is to simplify the expression as much as possible. Simplification means making an expression easier to read and work with without changing its value or meaning.
To simplify, start by ensuring all like terms are combined. If the result is \(9x + 4\), you've already simplified it significantly by combining \(2x\) and \(7x\) to become \(9x\).
Sometimes, simplifying might involve distributing and factoring, but in this case, combining terms is enough. Simplification helps you quickly understand and solve expressions, making mathematical tasks far easier to manage. This simplification sets the stage for further operations or equation-solving, where having clean and clear expressions can save time and effort.