Problem 84 - College Algebra

Question

What is a conditional equation? Give an example.

Step-by-Step Solution

Answer

A conditional equation is valid or true for certain values of the variable within the equation. An example would be \(x + 4 = 6\), which is only true when \(x = 2\).

Step 1: Defining a Conditional Equation

A conditional equation is an equation that is valid or true for certain values of the variable in it. These values that make the equation true are usually called solutions of the equation.

Step 2: illustrate by example

For instance, consider the conditional equation \(x + 4 = 6\). This equation is only true when \(x\) equals to 2.

Step 3: Testing an equation as Conditional

To ascertain if an equation is conditional, the given variable must be substituted with its value to check if it holds true. Substituting \(x = 2\) into the equation \(x + 4 = 6\), we have \(2 + 4 = 6\), which holds true, confirming our earlier assertion that \(x + 4 = 6\) is indeed a conditional equation.