Algebraic Equations Study Guide
What is an Algebraic Equation?
An algebraic equation is a mathematical statement that equates two algebraic expressions. It contains an equal sign and typically involves one or more variables. The goal is to solve for the value of the variable in the equation.Types of Algebraic Equations
There are several types of algebraic equations, including:- Linear Equations: These equations involve variables raised to the power of 1, and the highest power of the variable is 1.
- Quadratic Equations: These equations involve variables raised to the power of 2, and the highest power of the variable is 2.
- Cubic Equations: These equations involve variables raised to the power of 3, and the highest power of the variable is 3.
- Higher Order Equations: These equations involve variables raised to powers greater than 3.
Solving Algebraic Equations
To solve an algebraic equation, follow these general steps:- Combine Like Terms: Simplify both sides of the equation by combining like terms.
- Isolate the Variable: Use inverse operations to isolate the variable on one side of the equation.
- Check Your Solution: Once you find the value of the variable, plug it back into the original equation to ensure it satisfies the equation.
Common Techniques for Solving Equations
- Substitution: Replace a variable with an equivalent expression to simplify the equation.
- Factoring: Rewrite the equation in factored form to identify the roots or solutions.
- Completing the Square: Rearrange a quadratic equation to a perfect square trinomial to solve for the variable.
- Using the Quadratic Formula: This formula provides the solutions for a quadratic equation in the form ax^2 + bx + c = 0.
Practice Problems
Now that you have an understanding of algebraic equations, try solving the following practice problems:- Solve the linear equation: 3x + 5 = 2x - 3.
- Find the roots of the quadratic equation: x^2 - 4x + 4 = 0.
- Solve the system of equations: 2x + y = 7 and x - y = 1.
Summary
[Algebraic Equations] Related Worksheets and Study Guides:
.◂Math Worksheets and Study Guides Seventh Grade. Algebraic Equations
Study Guide
Algebraic Equations 
Activity Lesson
Algebraic Equations Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebra Skills Worksheet/Answer key
Algebraic Equations
Activity LessonWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Algebra (NCTM)
Use mathematical models to represent and understand quantitative relationships.
Model and solve contextualized problems using various representations, such as graphs, tables, and 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.