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### Course: Class 7 (Foundation)>Unit 8

Lesson 3: Equations

# 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.

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• 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.
• Variables

In mathematics, a variable is a symbol that represents an unknown value. Variables can be used to represent anything that can change, such as length, weight, or speed. They can also be used to represent unspecified quantities, such as the number of elements in a set or the number of pages in a book.

Expressions

An expression is a combination of numbers, variables, and mathematical operations. Expressions can be used to represent any value, such as the number 5 or the expression 2 + 3.

Equations

An equation is an expression that expresses the equality of two expressions. For example, the equation x + 2 = 5 means that the value of x is 3.

Differences between variables, expressions, and equations

Here is a table that summarizes the key differences between variables, expressions, and equations:

Attribute Variable Expression Equation
Definition A symbol that represents an unknown value A combination of numbers, variables, and mathematical operations An expression that expresses the equality of two expressions
Example x 2 + 3 x + 2 = 5
Purpose To represent an unspecified quantity To represent any value To express the equality of two expressions
For example, in the equation x + 2 = 5, x is a variable that represents an unknown value. The expressions x + 2 and 5 are mathematical expressions that represent the values 7 and 5, respectively. The equation as a whole means that the value of x is 3, since 3 is the only number that makes both expressions equal.

Variables can be used in expressions and equations.
Expressions can be used in equations.
Equations can be used to solve for variables.
• 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?
• An expression can be as simple as a number or a variable. Or, it can be a mix of numbers, variables, and math operations for addition, subtraction, multiplication and division. It will not have any equals symbol (=). Nor will it have any inequality symbol (>, <).

An equation requires 2 expression separated by an equals symbol (=).

An inequality also takes 2 expressions separated by an inequality symbol ("<", ">", "<=", ">=").

Hope this helps.
• whats the difference between an expression and an equation
• An expression can be as simple as a number or a variable. Or, it can include numbers, variables and symbols for addition, subtraction, multiplication and division. It will not have an "=" symbol or any type of inequality symbol.

An equation requires 2 expressions connect with an "=" symbol.

Hope this helps.