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High School Algebra II: Homework Help Resource26 chapters | 280 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Joseph Vigil*

In this lesson, you'll get a refresher on number sentences. You will then learn what equations are and how they can be useful in finding out missing information.

Let's say your goal is to complete three Study.com lessons per day for the next four days. To find the number of lessons you'll have completed after those four days, we'll of course need to add together all the lessons you complete. The addition will look like this:

3 + 3 + 3 + 3 = 12

Which we can rewrite as:

3 * 4 = 12

These are number sentences. A **number sentence** is a string of numbers, mathematical operations, and an equal sign that tell you a mathematical fact. Like a regular text sentence, it's a basic unit of information.

Here's another example of a number sentence:

(3 - 1) * 5 = 10

Again, we have a set of numbers and operations that gives a mathematical fact. If we subtract 1 from 3 and then multiply that difference by 5, we do indeed get 10.

What if we took away part of a number sentence? For example, let's say you know that you want to complete 12 lessons, and you know you have time to complete 3 per day. But you need to know how many days it'll take. So our number sentence now looks like this:

3 * ? = 12

All we've done is insert a question mark in the place of our unknown value. Now, there's nothing wrong with question marks, but in math, we normally use a **variable**, which is simply a letter that we use to stand in for an unknown value.

Since a variable is simply a placeholder, it doesn't matter what letter we use. For the sake of convention, however, you'll often see *x* used as a variable. If we do so here, then our number sentence looks like:

3 * *x* = 12

The letter *x* is the number of days you'll need to work. We now have an **equation**, which is a number sentence in which a variable takes the place of unknown information.

In other words, if you take out part of a number sentence and replace it with a variable, you've created an equation.

Let's look at a new scenario. You own a dog who had 11 puppies. You've decided you can afford to keep 2. How many would you need to give away?

Well, let's look at the number sentence we would normally create here. We're starting with 11, and we'll be subtracting an unknown number of puppies. That would leave us with the 2 puppies you can keep. So:

11 - ? = 2

Again, we'll put a variable in the place of our unknown value. Since we're dealing with puppies here, we'll use the variable *p*. (Remember, we can use any letter as a variable, although *x* is a very commonly used variable.)

11 - *p* = 2

We now have an equation that we could later solve to find that unknown value.

Example #2:

You've made $2,000 this month. Your rent payment is $800. You spend an average of $40 per day. How many days will your money last?

What we really need to do is take away (subtract) $800 from the original $2,000:

2,000 - 800

Then you'll need to divide the difference by some number of days to get 40.

(2,000 - 800) / ? = 40

Again, use a variable in place of the unknown value:

(2,000 - 800) / *x* = 40

We now have an equation that we can solve to determine the number of days your money will last.

Let's review.

An **equation** is simply a number sentence with a variable in the place of an unknown value. A **variable** is a letter that is substituted in place of the unknown value. It can be any letter you want, although *x* is most commonly used.

Number sentence | Equation |
---|---|

1+1 = 2 | 1 + x= 2 |

When you are done, you should be able to:

- Recall the difference between a number sentence and an equation
- Identify an equation and a variable

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22 in chapter 2 of the course:

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High School Algebra II: Homework Help Resource26 chapters | 280 lessons | 1 flashcard set

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations Containing Parentheses 6:50
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Equations with Multiple Steps 5:44
- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
- Standard Form: Equations & Formulas
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- What is an Equation in Math? - Definition & Examples 4:10
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