An equation is a condition on a variable. It is expressed by saying that an expression with a variable is equal to a fixed number, e.g. x – 3 = 10.

Explanation:

An equation is a mathematical statement that shows the equality between two expressions. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), which are separated by an equal sign (=). The LHS and RHS can contain variables, constants, and mathematical operations.

Condition on a Variable:

A condition on a variable refers to a constraint or requirement that must be satisfied by the variable in order for a given situation or statement to be true. It narrows down the possible values that the variable can take and helps in solving problems or determining solutions.

Example:

Let's consider the equation: x + 5 = 10.

In this equation, x is a variable. We can impose a condition on x to find its value. For example, if we want to find the value of x such that it is greater than 2, we can add the condition x > 2 to the equation. Now the equation becomes: x + 5 = 10, subject to x > 2.

By solving the equation with the given condition, we can find that x = 5 satisfies both the equation and the condition.

Importance of Conditions on Variables:

Conditions on variables are crucial in mathematics and problem-solving as they provide constraints that help in finding specific solutions or satisfying certain requirements. They narrow down the range of possible values for the variable and make the problem more manageable.

By imposing conditions on variables, we can eliminate extraneous solutions and focus on the values that meet the given criteria. This helps in solving equations, inequalities, and various mathematical problems.

Conclusion:

In the context of mathematics, an equation represents an equality between two expressions, while a condition on a variable is a restriction or requirement that must be satisfied by the variable. Therefore, an equation is not the same as a condition on a variable. The correct answer to the question is option B: equation.

An equation is a condition on a variable.

An equation is a mathematical statement that shows the equality of two expressions or values. It consists of an equal sign (=) between the left-hand side (LHS) and the right-hand side (RHS) of the equation. The LHS and RHS are composed of variables, constants, and mathematical operations.

Understanding Equations:
Equations are used to solve for unknown values in various mathematical problems. They represent a balance or relationship between the quantities involved. In an equation, the variable represents an unknown value that we are trying to find or determine.

Characteristics of Equations:
1. Equality: Equations show the equality between two expressions or values. The equal sign (=) indicates that both sides of the equation are equal.
2. Variables: An equation often contains one or more variables. Variables are represented by letters, such as x, y, or z. These variables can take on different values.
3. Constants: Equations may also include constants, which are fixed values that do not change.
4. Solving: The process of finding the value(s) of the variable(s) that satisfy the equation is called solving the equation. This involves performing algebraic manipulations to isolate the variable on one side of the equation.

Examples:
1. x + 5 = 10
In this equation, x is the variable, and the equation states that the sum of x and 5 is equal to 10. By subtracting 5 from both sides of the equation, we can solve for x: x = 10 - 5 = 5.

2. 2y - 7 = 3y + 2
This equation involves the variable y. To solve for y, we can start by subtracting 2y from both sides of the equation to eliminate the variable on one side: -7 = y + 2. Then, by subtracting 2 from both sides, we find y = -9.

Conclusion:
Equations are conditions on variables that express the equality between two expressions or values. They are an essential tool in mathematics for solving problems and finding unknown values.