Question
define Variable
Answers
GPT-4o mini
A variable is a symbolic representation used in mathematics, programming, and various sciences to denote a value that can change or vary. In a mathematical context, a variable often represents an unknown quantity in an equation or expression and can take on different values, typically denoted by letters such as \( x \), \( y \), or \( z \).
In the realm of programming, a variable serves as a storage location in memory that has a name (the variable's identifier) and can hold data values that may change during the execution of a program. The value assigned to a variable can be updated as the program runs, making variables fundamental for dynamic data manipulation.
In summary, a variable is:
- **Mathematically**: A symbol representing a quantity that can change.
- **Programmatically**: A named storage location in memory that can hold different values throughout the program's execution.
In the realm of programming, a variable serves as a storage location in memory that has a name (the variable's identifier) and can hold data values that may change during the execution of a program. The value assigned to a variable can be updated as the program runs, making variables fundamental for dynamic data manipulation.
In summary, a variable is:
- **Mathematically**: A symbol representing a quantity that can change.
- **Programmatically**: A named storage location in memory that can hold different values throughout the program's execution.
define Linear Equation in one variable
GPT-4o mini
A **linear equation in one variable** is an equation that can be expressed in the standard form:
\[ ax + b = 0 \]
where:
- \( x \) is the variable,
- \( a \) and \( b \) are constants, and \( a \neq 0 \).
In this equation, \( a \) represents the coefficient of the variable \( x \), and \( b \) is a constant term. The term "linear" indicates that the variable \( x \) is raised to the first power, meaning the graph of the equation will be a straight line when plotted.
To solve a linear equation in one variable, the goal is to isolate the variable \( x \) on one side of the equation. This typically involves performing algebraic operations such as addition, subtraction, multiplication, and division.
**Example**:
For the equation \( 3x - 6 = 0 \):
1. Add 6 to both sides: \( 3x = 6 \)
2. Divide both sides by 3: \( x = 2 \)
In this case, the solution to the linear equation is \( x = 2 \).
\[ ax + b = 0 \]
where:
- \( x \) is the variable,
- \( a \) and \( b \) are constants, and \( a \neq 0 \).
In this equation, \( a \) represents the coefficient of the variable \( x \), and \( b \) is a constant term. The term "linear" indicates that the variable \( x \) is raised to the first power, meaning the graph of the equation will be a straight line when plotted.
To solve a linear equation in one variable, the goal is to isolate the variable \( x \) on one side of the equation. This typically involves performing algebraic operations such as addition, subtraction, multiplication, and division.
**Example**:
For the equation \( 3x - 6 = 0 \):
1. Add 6 to both sides: \( 3x = 6 \)
2. Divide both sides by 3: \( x = 2 \)
In this case, the solution to the linear equation is \( x = 2 \).
-4/9x = - 36
GPT-4o mini
To solve the equation:
\[
-\frac{4}{9}x = -36
\]
we'll follow these steps:
1. **Isolate \( x \)**: To eliminate the fraction, multiply both sides of the equation by the reciprocal of \(-\frac{4}{9}\), which is \(-\frac{9}{4}\):
\[
x = -36 \times -\frac{9}{4}
\]
2. **Calculate \( x \)**:
\[
x = 36 \times \frac{9}{4} = \frac{36 \times 9}{4}
\]
\[
x = \frac{324}{4}
\]
3. **Simplify \( x \)**:
\[
x = 81
\]
Thus, the solution to the equation \(-\frac{4}{9}x = -36\) is:
\[
\boxed{81}
\]
\[
-\frac{4}{9}x = -36
\]
we'll follow these steps:
1. **Isolate \( x \)**: To eliminate the fraction, multiply both sides of the equation by the reciprocal of \(-\frac{4}{9}\), which is \(-\frac{9}{4}\):
\[
x = -36 \times -\frac{9}{4}
\]
2. **Calculate \( x \)**:
\[
x = 36 \times \frac{9}{4} = \frac{36 \times 9}{4}
\]
\[
x = \frac{324}{4}
\]
3. **Simplify \( x \)**:
\[
x = 81
\]
Thus, the solution to the equation \(-\frac{4}{9}x = -36\) is:
\[
\boxed{81}
\]