Equations

An equation is a mathematical statement that shows two expressions are equal. It contains an equal sign (=) and consists of two sides: the left-hand side and the right-hand side. The goal in solving an equation is to find the value of the variable that makes the equation true.

Types of Equations

There are various types of equations, such as:

Linear Equations: These equations have the highest power of the variable as 1, and can be represented in the form y = mx + b.
Quadratic Equations: These equations have the highest power of the variable as 2, and can be represented in the form ax^2 + bx + c = 0.
Exponential Equations: These equations involve exponential expressions, such as 2^x = 16.
Trigonometric Equations: These equations involve trigonometric functions, such as sin(x) = 0.5.

Solving Equations

To solve an equation, we perform operations on both sides of the equation to isolate the variable. The goal is to get the variable on one side of the equation and the constants on the other side. The operations used include addition, subtraction, multiplication, and division, as well as exponentiation and taking roots.

Study Guide

To understand equations better, follow these steps:

Learn the basic properties of equations, such as the meaning of the equal sign and how equations are used in real-life situations.
Understand the different types of equations and their representations.
Practice solving equations using various operations and techniques.
Explore applications of equations in different fields, such as physics, engineering, and finance.
Master the skills of solving equations with one variable and then progress to equations with multiple variables.

Remember, practice is the key to mastering equations. Try to solve different types of equations regularly to improve your skills.

◂Math Worksheets and Study Guides Sixth Grade. Algebraic Equations

The resources above cover the following skills:

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.