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### Course: Class 6 (Old)>Unit 7

Lesson 4: Solution of an equation

# Variables, expressions, & equations

In algebra, we use variables like x, y, and z to represent unknown values. Expressions are combinations of variables and numbers, while equations equate two expressions. Variables can take on different values depending on the context, and we can evaluate expressions by substituting values for the variables. Created by Sal Khan.

## Want to join the conversation?

• What's the difference between a variable and an expression?
• A variable is an unknown value. An expression is a way of expressing a concept using an unknown value (variable). Try re-watching the video if you still don't get it.
• When you evaluate x^y for x = -2 and y = 3, you should be careful to write it as (-2)^3 and not -2^3. Remember that exponents have precedence over subtraction, so the latter is not -2 x -2 x -2, but -(2 x 2 x 2). In this case, you get -8 either way, of course.
• u should go to math heaven cuz of that. that is to hard for me
• In the example x=-2 to the power y=3 you write -2^3 that is a mistake, the right way to do it is (-2)^3 ; because the "-" sign belong to the number "2". It is no the same:
(-2)^2=4 to -2^2=-4. Thanks so much for what you are doing.
• Can I point out this is 9 YEARS ago 9 years so about 2010
• In algebra, The letter X always appears. What does X represent?
• as said above, it is used to represent an unknown number. "Solving for x" means finding which number x represents. X can actually be any letter, but x is just the most common. For example, you could also "solve for a".
• I saw the video but I still don't understand. Can someone tell the difference between expressions, equations, and inequalities in a simpler way?
• Expressions have one or more terms which are separated by plus and minus signs. All we can do with these is simplify or evaluate for given values. Examples could include x, 3x + 2y, etc.
Next, we can set two expressions equal to each other by creating an equation. This will allow us to solve or isolate a variable. Examples could be 2x + 5 = 3x - 9 or y = 3x - 2. With two variables, an equation can be a function if each input (x in the equation above) has at most one output value (y in the equation above). With a single variable, the solution is a point on the number line, and with two variables it ends up as a line or curve on a Cartesian Plane.
The inequalities (greater than, greater than or equal to, less than, less than or equal to, and not equal to) allows for multiple solutions. On a number line, it creates ray(s) or a line, and it is an area on the Cartesian Plane. The equality part of the inequality would form a line or curve which could be solid or dashed and shading either above or below this line or curve.
• is it possible that there is so many variables in a equation that the problem is unsolvable
• No. It would only make the problem more complex not unsolvable.
• I JUST LOVE HOW WE HAVEN'T LEARNED THE SQUARE ROOT and it gives it to us here xD. So, basically the square root of something is the same thing as saying 9^1/2. That half just means taking the half of the exponent that 9^1 is equal to. Think of it like 9 = 3^2 = 3 x 3. This "^" sign is just means the number in front of it is exponent, we also refer it to "power of". So you have 3^2, which is equal to 3 x 3. If you take HALF of the exponent in the expression, which is 2, that is going to leave you with an exponent of 1, which is 3^1 = 3(or 1 x 3).
Another way to think of it, is 9^1 is equal to 3^2. 3^2 = 1 x 3 x 3. So what is half of what we are doing, which is multiplying 1 by 3 two times? Well, that's multiplying 1 by 3 only one time :), 1 x 3 = 3.
• So variables mean a mystery number or it can just sometimes be there and not mean anything in an equation
• A variable is a symbol with no fixed value. You'll see variables come in equations as anything.But, because they're letters, they have no fixed value. it not always equal to the same number; sometimes, it's not even equal to anything at all sometimes too.
• Where can we use Algebra in real life?
• We use Algebra to perform daily tasks such as baking a cake, finding out how much you spent this month and even general logical thinking.

Hope you found this helpful!
• I watched the video, but I'm still having a little trouble understanding what the difference is between an expression, inequality, and equation. Can someone explain it a bit simpler for me, please?