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## Operations and Algebraic Thinking 218-221

### Unit 5: Lesson 1

Algebraic equations basics

# Variables, expressions, & equations

Learn what variables, expressions, and equations are. 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.
• 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 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.
• How can you easily tell the difference between a variable, an expression, and an equation?
• A variable is used to represent something unknown. For example x, y, z

An expression does not have an equal sign. For example 4 + 10.

An equation is made up of 2 expressions and has an equal sign. For example 4 + 10 = 14
The provided text is a mix of instructional content and user comments from an educational platform, likely Khan Academy. It does not contain a structured mathematical question or a direct answer to a question.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

## Operations and Algebraic Thinking 218-221

### Unit 5: Lesson 1

Algebraic equations basics

# Variables, expressions, & equations

Learn what variables, expressions, and equations are. 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.
• 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 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.
• How can you easily tell the difference between a variable, an expression, and an equation?
• A variable is used to represent something unknown. For example x, y, z

An expression does not have an equal sign. For example 4 + 10.

An equation is made up of 2 expressions and has an equal sign. For example 4 + 10 = 14
user
The provided text is a mix of instructional content and user comments from an educational platform, likely Khan Academy. It does not contain a structured mathematical question or a direct answer to a question.

TYPE: NO_QUESTION