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Chapter 1: Problem 84

What is a conditional equation? Give an example.

Short Answer

Expert verified
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 by step solution

01

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.
02

illustrate by example

For instance, consider the conditional equation \(x + 4 = 6\). This equation is only true when \(x\) equals to 2.
03

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.

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Most popular questions from this chapter

In Exercises \(29-44,\) perform the indicated operations and write the result in standard form. $$5 \sqrt{-16}+3 \sqrt{-81}$$

What is a rational inequality?

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{1}{x+1}>\frac{2}{x-1} $$

Solve each rational inequality in Exercises \(29-48,\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ \frac{x+3}{x+4}<0 $$

Solve each quadratic inequality in Exercises \(1-28\) and graph the solution set on a real number line. Express each solution set in interval notation. $$ 3 x^{2}-5 x \leq 0 $$
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