What is a conditional equation? Give an example.

Verified step by step guidance

1. A conditional equation is an equation that is true for certain values of the variable(s) involved but not true for all values.
2. To understand this, consider the equation $x+3=5$.
3. This equation is only true when $x=2$.
4. If you substitute any other value for $x$, the equation will not hold true.
5. Thus, $x+3=5$ is a conditional equation because it is only true under the condition that $x=2$.

Key Concepts

Conditional Equation

A conditional equation is an equation that holds true for certain values of the variable(s) involved. Unlike an identity, which is true for all values, a conditional equation has specific solutions that satisfy the equation. For example, the equation 2x + 3 = 7 is conditional because it is only true when x = 2.

Solution Set

The solution set of a conditional equation is the collection of all values that make the equation true. In the case of the equation 2x + 3 = 7, the solution set consists of the single value {2}. Understanding the solution set is crucial for determining the specific conditions under which the equation is valid.

Graphical Representation

Graphical representation of a conditional equation involves plotting the equation on a coordinate plane to visualize its solutions. For instance, the equation 2x + 3 = 7 can be represented as a line, and the point where this line intersects the x-axis indicates the solution. This visual approach helps in understanding the relationship between variables and the conditions under which the equation holds true.