An equation is a mathematical statement that shows the equality of two expressions. It consists of two mathematical expressions, connected by an equal sign (=).

- Linear Equations: These equations have variables raised to the power of 1, and can be graphed as straight lines.
- Quadratic Equations: These equations have variables raised to the power of 2, and can be graphed as parabolas.
- Exponential Equations: These equations involve variables in the exponent, and often represent growth or decay.
- Trigonometric Equations: These equations involve trigonometric functions such as sine, cosine, and tangent.

To solve an equation means to find the value of the variable that makes the equation true. The goal is to isolate the variable on one side of the equation.

- Use the properties of equality to simplify both sides of the equation.
- Isolate the variable by performing inverse operations (opposite operations) to both sides of the equation.
- Check the solution by substituting the value back into the original equation to ensure it satisfies the equation.

Equations are often written using variables (like x or y) to represent unknown values. They can also include constants and coefficients.

For example, a linear equation in standard form looks like: ax + by = c, where a, b, and c are constants, and x and y are variables.

Equations are used in various fields such as physics, engineering, economics, and everyday life to model and solve real-world problems.

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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.