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Combining like terms is a fundamental skill in algebra. It helps to simplify expressions, making them much easier to handle in further calculations. To combine like terms, remember that these are terms within an expression that have the same variable parts. In our example, we are given the expression \[-7x + 11x.\] Here, both terms have the same variable, which is \(x\).
When identifying like terms, always check their variable and exponent. If these elements match, they can be combined. In this case, the terms' coefficients are all we need to adjust.To combine \(-7x\) and \(11x\), calculate the sum of the numerical coefficients. The key rule is: only coefficients are added or subtracted, while the variable part remains the same.

• Like terms: \(-7x\) and \(11x\)
• Coefficients to combine: \(-7 + 11\)
• Result: the terms combined give \(4x\)

Coefficients are the numerical part of the terms in an algebraic expression. They serve as multipliers for the variable component. Understanding how to work with coefficients is vital, as it lays the groundwork for combining like terms effectively.
In our expression, the coefficients are the values \(-7\) and \(11\). These tell us how many times each term's variable part is included.When working with coefficients, follow these steps:

• Identify them within the terms. Here, you find \(-7\) and \(11\) coupled with \(x\).
• Perform arithmetic operations like addition or subtraction only on these numerical parts. In this example, when you compute \(-7 + 11\), you simplify the expression to a single term of \(4x\).
• The result provides a simplified expression that's much easier to understand and use.

Variables are symbols used in algebraic expressions to represent numbers. They can vary and stand in place for unknown values. In our example, the variable \(x\) is used in both terms, which is why they're considered like terms.
Variables allow an expression to remain general, enabling multiple values to be used in calculations. This is particularly helpful in forming equations and solving problems with unknown quantities.Key points about variables:

• The variable component remains unchanged when combining like terms. For example, \(x\) stays as \(x\) regardless of changes in the coefficients.
• Variables can be any symbol (commonly \(x\), \(y\), \(z\)), but they hold meaning within the context of a problem.
• They provide the essence of algebra's flexibility, allowing us to develop formulas and solve equations.

Variables are what make algebraic expressions both powerful and versatile.