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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.

Watch this video lesson to learn how you can easily translate math sentences into inequalities. Once you know how to do this, solving word problems becomes that much easier.

Math sentences are also considered word problems because they are a mixture of numbers and words to put together. Your job is to understand the words and then turn them into a math problem that you can easily solve. This is the goal of this video lesson. We want to be able to take a **math sentence**, a sentence made up of numbers and words, and turn it into math symbols we can easily understand and solve algebraically. This particular lesson will focus on inequalities.

Usually in algebra, our goal is to find some unknown number. We will see how this plays out in our math sentences. I know you are getting worried about word problems, but you don't have to be afraid of them. Just keep watching, and you will see that they are not so bad. The key is in knowing how to translate some key words or phrases into math symbols as well as understanding the math behind the words. So let's get started!

We are talking about inequalities, so first I want to tell you the key phrases to look for that signal inequalities. We only have four phrases to look for: one phrase for each inequality symbol. We have the greater than symbol, the less than symbol, the greater than or equal to symbol and the less than or equal to symbol.

And yes, you are right. The key phrases we are looking for are simply the names of our symbols. If we are talking about the greater than symbol, then we will see the phrase 'greater than,' and if we are talking about the less than symbol, we will see the phrase 'less than.' Now let's see how these words work inside some real math sentences.

We have a math sentence that says the number of donuts that Chris has eaten is greater than 10. Our job here is to translate this into math symbols. What do we do? We first identify the important parts. Our important parts are the number of donuts eaten by Chris, the number 10 and the phrase 'greater than.'

We can label the number of donuts eaten by Chris with an *x* because that is our unknown number. We can label our phrase 'greater than' with our greater than symbol, >. Our 10 we will leave as 10. Now we can write our math sentence using math symbols: *x* > 10.

We can do a mental check to see if what we've written is the same as our math sentence. What we wrote down tells us that Chris is eating more than 10 donuts. Is this what our original sentence is also telling us? It is. So, we are right.

Let's see another sentence. The number of baby bunnies plus 5 is greater than or equal to 12. Our job here is to translate our math sentence into math symbols, and if we need to solve, to solve the problem the best we can. We begin by identifying our important parts and labeling them accordingly.

We have the number of baby bunnies, which we will label *x*. We have the word plus, which we will label +. Our numbers 5 and 12 stay as they are. The phrase 'greater than or equal to' we will label with its corresponding symbol. So, we have this: *x* plus 5 is greater than or equal to 12.

We see that we can solve it a bit more by subtracting the 5 from both sides to get our variable by itself. Doing that, we get *x* is greater than or equal to 7. And that is our answer.

Now, let's look at a problem using the less than or less than or equal to symbols. See if you can translate these on your own as we go along.

A number of donuts less 5 is less than 10. Here, we have a number of donuts, which we will label *x*. The word 'less' I will label with -. The 5 and 10 stay as they are. The phrase 'less than' is labeled with <. Now I have my math sentence of *x* - 5 < 10. I can solve this a bit more for my *x* by adding 5 to both sides. Doing that, I get *x* < 15 for my final answer.

Let's look at one more problem. One hundred cars is less than or equal to the number of trucks in Susie's garage. We keep our 100 as it is. The phrase 'less than or equal to' is labeled with its corresponding symbol. The number of trucks in Susie's garage is labeled with *x*. Our math sentence becomes 100 less than or equal to *x*, and we are done.

What have we learned now? We've learned that a **math sentence** is a sentence made up of numbers and words. To translate our math sentence into inequalities, we look for the keywords 'greater than,' 'less than,' 'greater than or equal to' and 'less than or equal to.' We match these with their corresponding symbols.

Other words, such as 'less' or 'plus,' we match with their corresponding subtraction and addition symbols. We label our unknown number with a variable, such as *x*. Once we have translated our math sentence, we see if we can solve it further to get the variable by itself. Once our variable is by itself, we are done.

After this lesson, you should have the ability to:

- Define the phrase 'math sentence'
- Identify the key words when translating inequalities
- Translate a math sentence involving inequalities and solve the inequality

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

- What is an Inequality? 7:09
- How to Graph 1- and 2-Variable Inequalities 7:59
- Set Notation, Compound Inequalities, and Systems of Inequalities 8:16
- Graphing Inequalities: Practice Problems 12:06
- How to Solve and Graph an Absolute Value Inequality 8:02
- Solving and Graphing Absolute Value Inequalities: Practice Problems 9:06
- Translating Math Sentences to Inequalities 5:36
- Go to High School Algebra: Working With Inequalities

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