An equation is a mathematical statement that shows the equality of two expressions. It consists of an equal sign (=) between two expressions, with one expression on the left side of the equal sign and the other expression on the right side. The expressions on both sides of the equal sign are called the "sides" of the equation.

There are different types of equations, including:

**Linear Equations:**Equations in which the highest power of the variable is 1. For example:*2x + 3 = 7*.**Quadratic Equations:**Equations in which the highest power of the variable is 2. For example:*x^2 - 4x + 4 = 0*.**Exponential Equations:**Equations in which the variable appears in the exponent. For example:*3^x = 27*.**Trigonometric Equations:**Equations involving trigonometric functions like sine, cosine, or tangent. For example:*sin(x) = 0.5*.

To solve an equation means to find the value of the variable that makes the equation true. Here are the general steps for solving an equation:

**Isolate the Variable:**Get the variable on one side of the equation by performing inverse operations.**Simplify:**Combine like terms and perform any necessary operations to simplify the equation.**Solve for the Variable:**Determine the value of the variable that satisfies the equation.**Check:**Substitute the value found back into the original equation to ensure it satisfies the equation.

When studying equations, it's important to understand the following key concepts:

- The meaning of an equation and its components (equal sign, expressions, sides).
- The different types of equations and their characteristics.
- The steps involved in solving equations.
- How to check the solution to an equation.

Practice solving equations of various types and difficulty levels to strengthen your understanding. Additionally, familiarize yourself with the properties of equality and the rules for manipulating equations.

Remember to always show your steps when solving equations to avoid making errors, and don't forget to check your solutions!

.Study GuideAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

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

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.