What exactly is x?

Question

This is a great question! What exactly is x?

This is one of, if not the most, common questions students have when first learning about algebra. That’s because algebra is the study of quantities and how they are related to other quantities. Their relationships are just as important—if not more important—than the actual numbers involved. This is why, in algebra, the elementary understanding of numbers is abandoned as the primary method of analysis. In other words, knowing the value of numbers is less important than knowing their relationship to other numbers.

This is why, in algebra, instead of using numbers such as 1, 2, or 3, we use symbols such as x, y, and z to represent any possible value.

Example:

Let’s say I have a basket of apples and a scale. For argument’s sake, the basket is weightless. I don’t know how many apples are in there, but I do know that each apple weighs about 5 oz (ounces).

I’ve already implied that I don’t know the number of apples I have, but I do know how much each apple weighs in ounces. I’ve implied that I know the numerical relationship between an apple and its weight in ounces.

Let’s continue and weigh this basket of apples. The scale tells me that the total weight of all the apples together is 30 oz. Thus, I have the following relationship:

Unknown number of apples × 5 oz = 30 oz

or, abandoning all units like ounces:

5x = 30

The asterisk (*) means to multiply. If each apple weighs 5 oz, then it would take a certain number of 5 oz apples to weigh a total of 30 oz.

x, in this case, represents the unknown number of apples in the basket. If I know that each apple weighs 5 oz, I can divide the total weight of the apples by 5 oz to find out how many apples I have:

5x ÷ 5 = 30 ÷ 5

x = 6

The reason I divided both sides by 5, instead of just the 30, is because I have to preserve the legitimacy of the equation. Think of it as a method of conservation. If 5x equals 30, and I only divided the 30 by 5, then the relationship between 5x and 30 would change, and 5x would now represent a smaller value. But all we know is that 5x = 30, not 5x = 6. The relationship would be compromised.

Instead, by dividing both sides, we’re saying that while x = 6 may look different compared to 5x = 30, the proportional relationship is preserved. The right side is still six times larger than the left. This is what matters most in algebra: the relationship. By performing the same operation on both sides, we conserve the proportionality of the equation.

In this specific problem, x = 6. This doesn’t mean that x = 6 in general. But based on the relationship between the apples and their weight, and the information we were given, x equals 6. Hence, we discovered that we have six apples without directly counting them.

You can verify this, too. If we did have six apples, that would mean the total weight of all the apples together is 30 oz:

6 apples × 5 oz per apple = 30 oz

What we’ve learned here about algebra is that it is useful for discovering unknown quantities based on their relationships to other quantities. We didn’t count how many apples there were, but by knowing the total weight and the weight of each apple, we were able to figure out how many apples were in the basket.

Answer 1

"X" is the twenty-sixth letter of the English alphabet.

In algebra it is used to represent an unknown value.

Answer 2

end of the alphabet is for variables unknowns, like x, y or z. during Thomas jefferson's presidency, they had the XYZ affair, involving unknown people in France.

beginning alphabet letters are for constants, known fixed numbers, a, b or c "just" arithmetic numbers

Answer 3

A variable is a placeholder, or what you are solving for. It is the "unknown."

Before the modern era, they had the concept of an unknown, but they didn't use variables. So, 2x + 3 would be stated the long way as "twice an unknown quantity plus three". Using variables just makes it a lot easier than stating is like that.

I love to think of "x" as the "X Box"!!! I put a box around my variable, and then I know it's a box that you can put values into and take values out of. It's just sitting there waiting to be filled with whatever you're solving for. So, x literally is the X-Box!

For example, x + 5 = 11. What can you put in the x-box to make the equation true? What do you add to five to make eleven? We don't know, so the box is empty, waiting for the value. Here, you may be able to guess it's 6. However, when you have a harder problem, you can still use methods you learn in algebra to get the box alone so you can see what to put in it to solve the equation.

Hope this helps!

Answer 4

x is a variable, which is a symbol that stands in the place of a number. It has no specific value, unless you are given one to substitute for it or if you are solving an equation. Although any letter or symbol can be a variable, x is the most popular, probably becomes it represents the domain when graphing.

Answer 5

Hello, thank you for taking the time to post your question!

You can think of “x” as being like a placeholder for the missing variable or unknown value that you are trying to solve for. So it allows you to set up expressions to solve for these unknown values.

I hope that helps get you moving in the right direction! Feel free to reach out if you still have questions beyond that :)