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Simplifying an expression is the process of making it easier to understand and work with. In algebra, this often involves reducing or eliminating parentheses and combining like terms. The goal is to write the expression in its simplest form.

To simplify an expression like \((3x - 5) - (7x - 11) - (5x + 2)\), you need to address each part step by step. Begin by eliminating the parentheses through operations such as distribution, if needed. Once those are gone, identify like terms. This means looking for terms that have the same variable raised to the same power and combining them.

By simplifying algebraic expressions, you make calculations more manageable and prepare the expression for solving equations or substituting values.

The distributive property is a key concept in algebra that allows you to simplify expressions and solve equations. It states that multiplying a number by a group of numbers added together is the same as doing each multiplication separately. In short, the rule is:

• \(a(b + c) = ab + ac\)

In the original exercise: \((3x - 5) - (7x - 11) - (5x + 2)\), you'll distribute the subtraction (negative sign) across the terms in each parenthesis.

For instance, subtracting \( (7x - 11) \) translates to distributing the negative sign as \(-1(7x - 11)\), which gives us \(-7x + 11\). Similarly, \( - (5x + 2) \) becomes \(-5x - 2\).

Distributing negative signs correctly is crucial as it changes the signs of the numbers and variables within the parentheses, leading to accurate expression simplification.

Combining like terms is another fundamental algebraic skill. Like terms are terms whose variables (and their exponents) are exactly the same. For example, \(3x\) and \(-7x\) are like terms, but \(3x\) and \(-7y\) are not.

Once you have an expression such as \(3x - 5 - 7x + 11 - 5x - 2\), your task is to gather and combine like terms. This involves:

• Adding or subtracting the coefficients of the terms with the same variables (e.g., \(3x - 7x - 5x\) combines to \(-9x\)).
• Adding or subtracting constant numbers (those without variables), like \(-5, 11,\) and \(-2\), resulting in \(4\).

The final expression, \(-9x + 4\), is simplified as it consolidates all similar terms into a clear, concise form. By mastering this skill, you can solve more complex equations efficiently.