In mathematics, a variable is a symbol that represents a quantity that can change or vary within a given context. Variables are used to denote unknown values in equations, expressions, and functions.

There are two main types of variables in mathematics:

**Independent Variable:**This is the variable that stands alone and isn't changed by the other variables you are trying to measure. It's usually denoted by x.**Dependent Variable:**This is the variable that depends on the independent variable. It's usually denoted by y.

Consider the equation y = 3x + 5. Here, x is the independent variable, and y is the dependent variable. The value of y depends on the value chosen for x.

When solving equations with variables, the goal is to find the value of the variable that satisfies the given equation. Here are the general steps to solve equations with variables:

- Isolate the variable by performing the necessary operations to get it by itself on one side of the equation.
- Perform the same operation on both sides of the equation to maintain equality.
- Simplify both sides of the equation until the variable is by itself on one side and the solution is on the other side.

Here are some key points to remember when studying variables in mathematics:

- Understand the difference between independent and dependent variables.
- Practice solving equations with variables.
- Learn to manipulate equations to isolate the variable.
- Work on real-life problems involving variables to understand their practical applications.

Understanding and mastering the concept of variables is crucial for solving mathematical problems and real-world applications. Practice and familiarity with the concept will lead to proficiency in handling variables in various mathematical contexts.

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Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.