Solving Equations

Solving equations is an essential skill in mathematics. It involves finding the value of the variable that makes the equation true. Equations are solved by performing operations to isolate the variable on one side of the equation.

Basic Steps for Solving Equations

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 answer: Substitute the solution back into the original equation to ensure that it satisfies the equation.

Types of Equations

There are different types of equations, such as:

Linear equations: Equations in the form ax + b = c, where a, b, and c are constants.
Quadratic equations: Equations in the form ax^2 + bx + c = 0, where a, b, and c are constants.
Literal equations: Equations involving several different variables.

Practice Problems

Let's solve some equations to practice the concepts:

Example 1: Solve for x in the equation 2x + 5 = 11.

Solution:

Subtract 5 from both sides to isolate x: 2x = 6
Divide both sides by 2: x = 3
Check the answer: Substitute x = 3 back into the original equation to ensure that it is true: 2(3) + 5 = 11, which is true.

Example 2: Solve for y in the equation 3y - 7 = 20.

Solution:

Add 7 to both sides to isolate y: 3y = 27
Divide both sides by 3: y = 9
Check the answer: Substitute y = 9 back into the original equation to ensure that it is true: 3(9) - 7 = 20, which is true.

Summary

In summary, solving equations involves performing operations to isolate the variable and find its value. It is important to carefully follow the steps and check your answers to ensure accuracy.

Now that you have a solid understanding of solving equations, it's time to practice and master this fundamental skill in mathematics!

◂Math Worksheets and Study Guides Seventh Grade. Algebraic Equations

The 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.