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Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

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Lesson Transcript

Instructor:
*Yuanxin (Amy) Yang Alcocer*

Amy has a master's degree in secondary education and has taught math at a public charter high school.

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.

**One-step algebra equations** are actually very nice to work with. Why is this? These are equations that only require one operation to solve. Your one step will be addition, subtraction, multiplication, or division. You only need to do one of these operations. They are quick and easy!

In math, sometimes, you will see our one-step algebra equations in the form of **word problems**, equations written out in English instead of math. I know word problems are considered monsters, and students fear these, but they really are not that bad to work with. The key lies in translating the word problem using the correct math symbols and writing our math symbols in the right order.

Let's look at an example to see how translating a word problem into math symbols works.

Our problem says, 'Solve four less than a number equals eight.'

We begin by highlighting our important words. We look for words that show our numbers and also words that show operations. As you read, think about what the words and phrases mean, and if they can be translated into math symbols. In our problem, we have the words four, less than, a number, equals, and eight. I go ahead and highlight all these words and phrases. I can also write the math symbols for these words next to their highlights. I know what four and eight are without thinking. So I write 4 and 8 next to those words. The phrase 'less than' translates into subtraction because for something to be less than something, it needs to be subtracted. So I write a minus sign next to that word. Now I need a math symbol for the phrase 'a number.' What is a number? I don't know what that number is, so that tells me that this is the part that the problem is asking me to solve. So I use the most famous algebra variable of *x* to represent this number that I need to solve for. Lastly, for the word equals, I am going to write down the equals symbol.

Now, I need to figure out the order these math symbols need to be written in. It might be tempting to write them down as they appear in English, but that would be wrong. The way the symbols appear right now is 4 - *x* = 8. But this doesn't mean the same thing; it's wrong. This is where you have to be careful. The phrase 'less than' is a bit tricky. You have to think, what is less than what? It says that the four is less than a number. You have to ask yourself, which is the larger value and which value is being subtracted from the larger value? When it says that four is less than a number, that tells me that the number is larger and that the four is being subtracted from that number, so in math, I would have to write *x* - 4. The larger number comes first in math. In English, it's backwards. So my correct math translation is *x* - 4 = 8.

Once I have translated my word problem correctly, I can go ahead and solve it. To solve my problem, *x* - 4 = 8, I need to isolate the variable. To do this, all I need to do is to move the -4 to the other side. To do that, I just need to add four to both sides. Doing this, I get *x* - 4 + 4 = 8 + 4 which turns into *x* = 12, and I have my answer.

What have we learned? We've learned that **one-step algebra equations** are equations that only require one operation to solve and that **word problems** are math problems written in English. Solving these problems requires you to translate your words into math symbols. The way to do this is to think of the meaning behind the words and then write down the matching math symbols.

One thing to keep in mind when you are translating a word problem into a math equation is to think of the English meaning of the word because sometimes the English meaning is backwards from the way it is translated into math. For example, the phrase 'less than' switches the values. Saying 'eight less than 12' translates into 12 - 8 and not 8 - 12. If we said, 'we have eight, take away four,' instead, then the order would stay the same because the meaning behind those words means that I am taking four away from eight which translates into 8 - 4. Just read carefully. Once you've translated the word problem, the easy part is to solve it. Perform the right math operation, and you are done!

After you have finished with this lesson, you'll be able to:

- Define one-step algebra equations and word problems
- Explain how to translate word problems into math equations
- Identify words or phrases that can be tricky when doing this translation

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Algebra I: High School20 chapters | 168 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
- Solving Equations with Infinite Solutions or No Solutions 4:45
- Translating Words to Algebraic Expressions 6:31
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
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