Inequalities are math statements that present a level of order between two algebraic expressions or values. As the name implies the relationship that is present is not equal otherwise it would be an equation. The relationship can be defined as one side of the statement being greater than or lesser than. It can also be a relationship that has a level of tolerance from being balanced. As a result, the relationship can also be described as greater than or equal to. It can also be described as less than or equal to. This form of math is really helpful to describe real life situation and model all forms of algebra. In this section you will find a number of worksheets and lessons that will help you learn how to use this type of math to find solutions to all different types of problems.
- Creating Equations and Inequalities - You will be given a story-based problem and asked to model the situation with math. Once you complete this section you will quickly realize that you encounter situations like this almost on a daily basis.
- Graphing Linear Inequalities as a Half-Plane - This can be used to help us predict possible outcomes. We show you not only how to visualize these on a graph, but also how to indicate where the answer would logically fall.
- Inequalities and Numbers Lines - A good way to help students understand what an inequality means. Using a numbers line really helps stimulate their brains to think about where this fits in.
- Inequality Constraint or Condition Word Problems - These are used in science to model preset conditions. This topic will help students better understand when this type of data modelling is useful to better understand trends.
- Solve One-Variable Equations and Inequalities - The first step in breaking down these types of problems. This topic really helps students understand the meaning of the data that they are manipulating.
- Solving Equations and Inequalities - These move students into a more complex situation. We are focusing on how to interpret possible solutions and see if they make sense and fit the models that are already in place.
- Solving Linear Equations and Inequalities in One Variable - You are only missing a single piece to solve these. With these problems we are focused on rearranging equations and inequalities to make them work for us.
- Word Problems Leading to Inequalities - In these types of problems, you will be predicting a chance of something happening. You are not looking for a finite solution, but rather a circumstance that agrees with the model.
- Word Problems That Require Equations or Inequalities - You will need to model the situation in order to help you make a predicted outcome. Your end goal is to find a slice of data that satisfies a potential outcome.
What are Inequalities?
Most of the mathematical problems are solved for the exact solutions. We use equals to '=' sign for such answers, to represent that two things or values are equal. However, with some math problems, you only need to tell whether one thing is smaller, greater or equal to something else. Or maybe you only need to tell that two things are not the same. These problems or mathematical cases are known as inequalities.
Inequalities are used to tell the relative size of two things. These are also used to represent the relationship between two expressions or numbers. Inequality is used when the value is:
Greater than the other value (a > b represents that a is greater than b)
Smaller than the other value (a < b represents that a is smaller than b)
Not greater than the other value (a ≤ b represents that a is not greater than b, or it is equal or smaller than b)
Not smaller than the other value (a ≥ represents that a is not smaller than b, or it is equal to or greater than b)
Not equal to the other value (a ≠ b represents that a is not equal to b) Inequalities are often over looked as far as their level of importance in real world math. The truth is that most fields that use inequalities on a daily basis are seen as your more prestigious careers.
Tips for Writing Inequalities to Model Math Based Situations
There are many different situations where you can use your math skills to better understand your environment or an event in time. The most important concept you need to start with is understanding the context of an inequality. They will help us model events where we are not trying to be exact, rather we are trying to understand a data trend that it presents. There are many financial transactions that we use this form of modeling to understand if we have enough or extra capital that we can apply to secondary transactions. If we look at a typical transaction that most teenagers find themselves in, we can start to see how this applies. What if Jim wanted to know how many hours, he needs to work in order to buy a pair of over the ear headphones to study with. We would need to know where Jim stands financially and how much he earns at his job. If Jim earns nine dollars an hour at his job and has thirty-five dollars saved up, that give us a good starting point. We then have to understand how much these headphones cost. If tax were to be included, the headphones cost one-hundred and fifty-three dollars. With all of this information, we can quickly create an inequality. We first would represent the number of hours Jim needs to work with the term 9h. 9 indicating the amount he is paid per hour and the variable h indicating how many hours he would need to work. We then represent the constant which is the amount of money he already has with 35. Putting those terms together, we have the start of our inequality as: 9h + 35. We then have to represent the amount he needs to accumulate: 153. He needs to have that amount money or more to buy the headphones. We would represent this with a symbol that implies he has an equal amount or more with the symbol (≥). Putting it all together we would have modeled the transaction as: 9h + 35 ≥ 153. To find the number of hours he needs to work, we would need to rearrange it to isolate the number of hours. We can do this by making sure that perform the operations on both sides of the symbol ≥ . First we would get rid of the constant by subtracting both sides by 35. That would leave us with: 9h ≥ 118. We would then divide both sides by 9. That would leave us with: h ≥ 13.11. This means that Jim would need to work at least 13.11 hours to buy his headphones.