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Ch 14: Overview of Algebraic Equations

About This Chapter

This chapter provides an overview of algebraic equations. Get familiar with the use of the addition principle for solving equations, the purpose of the distance formula, and more.

Overview of Algebraic Equations - Chapter Summary

Here, you will be presented with an overview of algebraic equations. Look at information about word problems with multi-step algebra equations, the process of solving equations that contain parentheses, and the steps necessary to find the volume of spheres, cones, and cylinders. See other information on algebraic equations, such as:

  • Linear, polynomial, quadratic and more common algebraic equations
  • Definition, translation, and solutions for one-step equations
  • Use of the multiplication principle to solve equations
  • The collection of like terms on one side of the equation
  • Solutions for equations that have infinite or no solutions
  • Word problems with one-step algebra equations
  • Use of the midpoint formula
  • Finding the perimeter of rectangles and triangles
  • Circumference and area of circles

These video lessons average 5-10 minutes in run time. Lessons are hosted by Study.com instructors, and each has its own quiz to test your understanding of the material. We include a video transcript and keyword-based timeline tool as study aids.

15 Lessons in Chapter 14: Overview of Algebraic Equations
Test your knowledge with a 30-question chapter practice test
Common Algebraic Equations: Linear, Quadratic, Polynomial, and More

1. Common Algebraic Equations: Linear, Quadratic, Polynomial, and More

Watch this video lesson to see the kinds of equations that you will come across most often in algebra. Learn to distinguish them by just looking for the identifying components of each equation.

Defining, Translating, & Solving One-Step Equations

2. Defining, Translating, & Solving One-Step Equations

Watch this video lesson to learn how you can write a simple math equation when you are given a word problem. Learn how to translate words into math symbols. Learn the shortcuts to remember.

Solving Equations Using the Addition Principle

3. Solving Equations Using the Addition Principle

In algebra, we have certain principles that we use to help us solve equations quickly and easily. The addition principle is one of them. Watch this video lesson to learn how you can apply it to solve your equations.

Solving Equations Using the Multiplication Principle

4. Solving Equations Using the Multiplication Principle

When it comes to solving equations in algebra, one of the essential skills you need is the ability to multiply. Watch this video lesson to learn how you can use the multiplication principle to isolate your variable.

Solving Equations Using Both Addition and Multiplication Principles

5. Solving Equations Using Both Addition and Multiplication Principles

Most times in algebra, to solve for your variable, you will need to perform more than one operation to get your answer. Watch this video lesson to learn the proper steps to take to solve these equations.

Collecting Like Terms On One Side of an Equation

6. Collecting Like Terms On One Side of an Equation

When you are using algebra to solve your problems, one of your biggest and most often used methods is that of collecting like terms. Watch this video lesson to see how it is done.

Solving Equations Containing Parentheses

7. Solving Equations Containing Parentheses

When we have parentheses in our equations it changes the way we solve them. Now we have an added step to do to remove those parentheses. Watch this video lesson to learn how it is done.

Solving Equations with Infinite Solutions or No Solutions

8. Solving Equations with Infinite Solutions or No Solutions

In algebra, there are two scenarios that give us interesting results. Watch this video lesson to learn how you can distinguish problems that have no answers and problems that have an infinite number of answers.

How to Solve One-Step Algebra Equations in Word Problems

9. How to Solve One-Step Algebra Equations in Word Problems

Word problems may be considered the most evil math invention ever, but never fear! Just watch this video lesson and you will know how to methodically translate these word problems into simple math and then to solve it.

How to Solve Multi-Step Algebra Equations in Word Problems

10. How to Solve Multi-Step Algebra Equations in Word Problems

After watching this video lesson, you will be able to solve word problems like a pro. Learn how to setup your problem, write your equations and then solve your equations to find your answer.

How to Use The Distance Formula

11. How to Use The Distance Formula

You can't always rely on your smartphone to tell you how far you need to travel to get from point A to point B. The distance formula will tell you the distance between any two points on a graph. In this lesson, you'll learn where it comes from and how to use it!

How to Use The Midpoint Formula

12. How to Use The Midpoint Formula

The formula for the midpoint of a line segment will tell you how to find the middle of any line segment on the x, y plane. Learn about this formula and see how it is used to find the midpoint of a line segment.

Perimeter of Triangles and Rectangles

13. Perimeter of Triangles and Rectangles

Without realizing it, we calculate and use the perimeter of triangles and rectangles in regular everyday situations. Learn more about the perimeter of triangles and rectangles in this lesson, and test your knowledge with a quiz.

Circles: Area and Circumference

14. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

Volume of Cylinders, Cones, and Spheres

15. Volume of Cylinders, Cones, and Spheres

In this lesson, we'll learn about the volume formulas for cylinders, cones and spheres. We'll also practice using the formula in a variety of real-world examples where knowing how to calculate volume is helpful.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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