In our daily lives, the terms equality and inequality seem very simple. It’s common knowledge that equal means two (or more) things are the same. They could be equal in size, cost, or any other characteristic. Inequality means two (or more) things are not equal. They differ in size, shape, cost, or some other characteristic. Easy enough, right?
But what do equality and inequality mean in mathematics? In the mathematical world, equality is a foundational topic, particularly in algebra. Mathematical equations use the symbol (=) to show equality between two quantities. An example of this would be 3 + 4 = 7. When you solve one side, you will see that it is the same, or equal, to the other. On the other hand, inequality compares two unequal sides with a different symbol showing the relationship. Let’s dive in deeper!
Equality
Equality can be as simple as 3 +4 = 7 or as complex as x = 2y. We can say that a = b so in turn b = a. But what if a also equals c? This now means that b also equals c. Equality can be shown in different ways and it’s important to understand that it is not always as simple as 3 + 4 = 7.
You may find yourself solving a problem where a = 2b and b = 4. Now you must plug in the information provided to find the solution: a = 2(4) so a = 8. The basic concept of equality is important to understand as it is the basis for a large amount of the topics school children will cover in math class and throughout their education.
Inequality
Now that we understand equality, what exactly is inequality? Although it simply means what is not equal (unequal), it goes much further than just that. When two things are unequal, they are not the same. An apple and an orange are not the same. The numbers 6 and 7 are not the same. But how do we show this relationship in mathematics? We do this by using mathematical symbols – a good alternative.
When two things are definitely not equal, we can use the symbol ≠. Using the unequal symbol would look like this: 8 +5 ≠ 20. What if we want to show which side is larger? When showing the relationship between two unequal sides, we can use the symbols ＞ and ＜. But which symbol do you use to show “greater than” and which symbol do you use for “less than”? The easiest way to remember is that the open side of the arrow will be on the greater than side. Like so: 6 ＞5.
The larger side to the larger number, the smaller side to the smaller number. This applies to more complex equations as well, such as x + 7 ﹥ 12. This would tell us that x ﹥ 5, so even 5.01 would make the equation true. Let’s try it out: 5.01 + 7 ﹥ 12 comes out to 12.01 ﹥ 12, making the equation true.
Let’s take this one step further. What if we need to show that something needs to be less than one number, but greater than another? We would still use the symbols shown above but we can expand the equations and include multiple symbols. If we need x to be less than 10 but greater than 1, we can display the relationship like this 1 ＜ x ＜ 10. To understand this, you can read both sides of the equation separately and then, when combined, they give us the full picture.
Now, what do we do if something is greater than or equal to the other side, and less than or equal to the other side? Luckily, there are symbols to show that as well. To show “greater than or equal to”, use the symbol ≥. To show “less than or equal to”, use the symbol ≤. Let’s try this out with the equation previously shown above. If x ≥ 5, then we can say that x + 7 ≥ 12.
Now let’s put this into a real-life example – such as a bag of marbles. If there are 7 marbles in the bag and more than 5 are added in, there are more than 12 in there now. We could apply “less than” to this as well: x+ 7 ≤ 12, so x ≤ 5. If fewer than 5 marbles were added to the bag of 7, then there are fewer than 12 marbles in the bag.
At OMC
As you can see, the topic of equality and inequality has more to it than meets the eye. It is a crucial notion to understand as it is a basic concept particularly important in algebra. At OMC, we ensure that all students leave school with a solid education of math concepts such as these, and the ability to use the concepts that they have been taught in the classroom. Whether it comes naturally to a student or not, we offer classes and tutoring that can assist them in strengthening their foundation in mathematics. OMC works to ensure that every student reaches or surpasses their full potential.
Contact OMC today to help ensure your child gains a solid, complete understanding of the most important mathematical concepts, such as equality and inequality, by signing them up for classes that are tailored to their specific educational needs.
