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To understand the nature of algebraic expressions, think of them as phrases that represent numerical relationships. These expressions can include numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, or division. However, a key characteristic of an algebraic expression is that it does not contain an equals sign (=).

For example, consider the expression 4x + 2. Here, we have the variable (x), which might stand for any number, and it is being multiplied by 4, then 2 is added to the product. This expression can be seen as a recipe for producing a numerical value, based on the value assigned to (x). Algebraic expressions are the building blocks of equations and can be as simple as a single number or as complex as a long combination of terms.

Now, let's move on to solving equations. The process of solving an equation involves finding the value(s) of the variable(s) that make the equation true. Solving an equation is akin to solving a puzzle: you're trying to find the missing piece (the value of the variable) that makes everything fit perfectly.

Take the equation (x + 3 = 7), for instance. To solve this, you would perform operations that would isolate the variable (x) on one side of the equals sign, leading you to discover that (x = 4) is the solution. During this process, whatever you do to one side of the equation, you must do to the other side to maintain the balance that equations conceptually represent.

Mathematical statements are sentences that express an idea or relationship in mathematics. They can either be true or false, but not both. Equations are a type of mathematical statement that declares the equality between two expressions, indicated by the presence of an equals sign (=).

In the given step by step solution, the mathematical statement (6-4x=7) includes numerical values, a variable, arithmetic operations, and most importantly, an equals sign, establishing it as an equation. This equation asserts that when 4 times a certain number (represented by (x)) is subtracted from 6, the result should be equal to 7. Understanding the nature of the given statement is essential in determining the appropriate methods used for finding solutions and delving into deeper algebraic concepts.