A linear equation in one variable is a fundamental concept in algebra. It is an equation that contains only one unknown variable, and this variable is raised to the first power only. The standard form is a x plus b equals zero, where a is not equal to zero, and x is the variable we want to solve for.
Linear equations have several key characteristics. They contain only one variable, and this variable always has a degree of one. There are no products of variables, no square roots, and no fractions containing the variable. When graphed, a linear equation always produces a straight line.
To solve a linear equation, we follow three main steps. First, isolate the variable term by moving constants to the other side. Second, divide both sides by the coefficient of the variable. Third, always check your solution by substituting back into the original equation. Let's solve three x plus six equals zero as an example.
Linear equations have many real-world applications. They are used in distance and speed problems, age problems, money and pricing calculations, temperature conversions, and simple interest calculations. For example, if a taxi charges three dollars plus two dollars per mile, and the total cost is fifteen dollars, we can use the equation three plus two x equals fifteen to find that six miles were traveled.
To summarize what we have learned about linear equations in one variable: They contain one variable with degree one, follow the standard form a x plus b equals zero where a is not zero, are solved by isolating the variable, and are widely used in real-world problem solving.