Equations and Variables in Algebra

Questions and Answers

An equation (correct)

A quadratic function

A linear expression

A variable

Quadratic equation (correct)

Simple equation

Linear equation

Exponential equation

A variable that changes in response to another variable

A variable that changes freely (correct)

A variable that is never used

A variable that is always constant

It can only take on specific, distinct values Signup and view all the answers

They allow us to generalize and model real-world situations Signup and view all the answers

To model and solve problems in various fields Signup and view all the answers

Study Notes

A statement that says two mathematical expressions are equal
Typically written with an equal sign (=) separating the two expressions
Examples:
- 2x + 3 = 5
- x^2 - 4 = 0
Can be:
- Simple equations: only one variable and no exponents (e.g., 2x = 4)
- Linear equations: degree of the variable is 1 (e.g., 2x + 3 = 5)
- Quadratic equations: degree of the variable is 2 (e.g., x^2 - 4 = 0)

A symbol that represents a value that can change
Often represented by letters (e.g., x, y, z)
Can be:
- Independent variable: changes freely (e.g., x in the equation y = 2x)
- Dependent variable: changes in response to the independent variable (e.g., y in the equation y = 2x)
Variables can be:
- Discrete: takes on specific, distinct values (e.g., whole numbers)
- Continuous: takes on any value within a certain range or interval (e.g., real numbers)
Importance of variables:
- Allow us to generalize and model real-world situations
- Enable us to solve problems and make predictions

Defined as a statement that equates two mathematical expressions
Typically denoted by an equal sign (=) separating the two expressions
Examples of equations include:
- Simple equations with one variable and no exponents (e.g., 2x = 4)
- Linear equations with a degree of 1 (e.g., 2x + 3 = 5)
- Quadratic equations with a degree of 2 (e.g., x^2 - 4 = 0)

Represented by symbols, often letters (e.g., x, y, z)
Can be independent or dependent
- Independent variables change freely (e.g., x in y = 2x)
- Dependent variables change in response to the independent variable (e.g., y in y = 2x)
Variables can be:
- Discrete, taking on specific, distinct values (e.g., whole numbers)
- Continuous, taking on any value within a certain range or interval (e.g., real numbers)
Importance of variables:
- Allow generalization and modeling of real-world situations
- Enable problem-solving and prediction