Problem 75 - College Algebra

Question

What is a linear equation in one variable? Give an example of this type of equation.

Step-by-Step Solution

Answer

A linear equation in one variable is expressed in the form \( ax + b = 0 \), where 'a' and 'b' are real numbers, and 'a' ≠ 0. An example is \( 3x - 7 = 0 \).

Step 1: Define a Linear Equation

A linear equation in one variable is an equation that can be expressed in the form \( ax + b = 0 \), where 'a' and 'b' are real numbers, and 'a' is not equal to zero. The 'x' is the variable.

Step 2: Understand Characteristics of a Linear Equation

In this type of equation, when graphed, it represents a straight line. The variable 'x' has the power of 1 (any other power would mean it's a different type of equation). 'a' is known as the coefficient of 'x' and 'b' is a constant.

Step 3: Create an Example

An instance of a linear equation in one variable could be something like \( 3x - 7 = 0 \). Here 'a' is 3, 'b' is -7, and 'x' is the variable we solve for.