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When we talk about simplifying expressions in algebra, we mean making them as neat and straightforward as possible. An algebraic expression can have numbers, variables, and operators like addition or subtraction. To simplify these, we look for opportunities to make calculations easier and to reduce the number of terms.You might wonder why simplifying is important. Well, a simplified expression is easier to work with, especially in further complicated calculations or graphing. It reveals the underlying math in a clearer way and helps us focus on the essential parts.The original problem presented was to simplify the expression \(7x + 4(x-6)\). The process involves using mathematical rules like the distributive property and combining similar terms to reduce it to \(11x - 24\). This makes it much simpler to evaluate if you substitute a value for \(x\), or to compare with other expressions.

The distributive property helps in breaking down expressions that involve both multiplication and addition or subtraction. It is crucial for spreading out multiplication over a sum or a difference inside parentheses.Here's how it works: If given an expression like \(a(b + c)\), the distributive property lets you multiply \(a\) with each term inside the parenthesis separately. Thus, \(a(b + c) = ab + ac\). This property is especially helpful in making expressions more manageable.Taking our example \(7x + 4(x - 6)\):- The \(4\) in front of the parentheses multiplies each item inside. - So, we calculate \(4 \cdot x\) and \(4 \cdot -6\), resulting in \(4x\) and \(-24\).Applying the distributive property transformed the expression to \(7x + 4x - 24\), which is much easier to manage.

Combining like terms is a method that allows us to simplify expressions by adding or subtracting terms that have identical variables and exponents. This helps cluster similar elements into one, reducing the complexity of expressions.When looking at the expression \(7x + 4x - 24\), the two terms involving \(x\), namely \(7x\) and \(4x\), are considered like terms.- Both terms have the same variable, \(x\), with the same power, which is 1. - Therefore, they can be combined to form a single term: - Simply add the coefficients 7 and 4, giving \(11x\).After combining these terms, the expression simplifies to \(11x - 24\), showing how straightforward the result becomes when like terms are carefully combined.