# Solving One-Step Linear Inequalities Video

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• 0:01 Linear Inequalities
• 1:40 Solving by Subtraction
• 3:24 Solving by Division
• 4:55 Solving by Multiplication
• 6:04 Lesson Summary
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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.

In this video lesson, you will learn how you can solve any kind of linear inequality that only requires one step. Learn when you need to subtract, when you need to add, when you need to multiply, and when you need to divide.

## Linear Inequalities

Linear inequalities are linear equations with inequality signs instead of equal signs. They compare two different quantities. In math, the linear inequalities that you will come across will usually involve a variable that you need to solve for. You will find these linear inequalities not just in math, but also in use in the real world. You can ask a medical doctor how tall most people are and he might show you a chart and tell you that most people are less than 7 feet. What he has just told you is a linear inequality in words. If we represented a person's height with x, we can write x < 7 feet to show that his height is less than 7 feet. And there we have our linear inequality. It is linear because our variable doesn't have any exponents, or, in other words, has an exponent of 1 (in math, no exponent means there is an exponent of 1 that is not written). We have our 'less than' inequality sign and we have the other side of our inequality, the 7. What we have here is a complete inequality statement because we know exactly what values our x can take (any number less than 7). However, there will be times where you have a problem such as x + 3 < 10 where you need to solve the problem to find out what our x values are.

## Solving by Subtraction

In this first example that we are looking at, we see that our x has a plus 3 attached to it. When we see an addition problem like this, we solve it by subtracting the number that is being added. Remember, if you do one operation to one side of an equation or inequality, then you must do the same to the other side. So for the problem x + 3 < 10, we subtract the 3 from both sides of the inequality to solve. We get x + 3 - 3 < 10 - 3 which turns into x < 7. And there we have our answer.

Do you see what we did? We actually performed the opposite operation that we saw to solve our inequality for our variable. Remember that when we solve for a variable, we want to get our variable by itself.

Now, if we had a subtraction problem, we would perform the opposite operation to solve it just like we did for the addition problem. So, if we see a problem such as x - 8 > 10, we would add the 8 to both sides of the problem. What do we get? We get x - 8 + 8 > 10 + 8 which turns into x > 18. Our answer is x > 18, or all numbers greater than 18.

Since this lesson is all about linear inequalities that only require one step to solve, we won't talk about the situation where our x is the one being subtracted. That requires two steps and is covered in another lesson.

## Solving by Division

If we had a problem such as 4x > 20, what do you think we need to do? That's right; we need to divide, because division is the opposite of multiplication. So, we divide both sides by 4. We get 4x/4 > 20/4 which becomes x > 5.

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