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Understanding the properties of equality is crucial when approaching algebraic problems. These properties are the ground rules that allow us to manipulate equations and maintain their balance. One fundamental aspect of these properties is that whatever operation you perform on one side of an equation, you must do the same to the other side to keep the equation true.

For instance, the Subtraction Property of Equality that we see in the exercise is used to subtract the same value from both sides, ensuring the balance is preserved. Other properties include the Addition Property of Equality, Multiplication Property of Equality, and Division Property of Equality. These properties are not only useful in solving linear equations but are integral to understanding the logical structure of algebra.

Solving linear equations is a foundational skill in algebra. The goal is to find the value of the unknown variable that makes the equation true. To do so, we often use the properties of equality to systematically perform operations that simplify the equation and isolate the variable.

The exercise provided demonstrates a simple linear equation. By applying the Subtraction Property of Equality, we reduce the equation to its simplest form to find the solution for the variable. In more complex equations, we might combine multiple properties of equality and use additional techniques such as distributing, combining like terms, and factoring.

Algebraic expressions are combinations of variables, numbers, and operations that represent a specific quantity. Unlike equations, expressions do not have an equals sign. When solving equations, we often manipulate algebraic expressions on either side of the equation to simplify them and solve for the variable.

In the given exercise, the expression on the left side of the equation consists of a variable and a number. Solving the equation involves understanding how to properly manipulate this expression using the properties of equality without losing the meaning of the original problem. Mastering the manipulation of algebraic expressions is key to excelling in algebra and more advanced mathematics.