Solving Linear Equations with One Unknown

Study Notes

Solving Equations with One Unknown: Linear Equations

Solving equations can be an essential skill for various fields, such as mathematics, science, engineering, and economics. In this article, we will focus on solving equations with only one unknown variable, which is typically represented by a letter, usually x. These types of equations are called linear equations because their terms have only a first power.

A linear equation is an algebraic equation in which each term is either constant or has degree 1, meaning it's a first-degree polynomial. An example of a linear equation would be ax + b = c, where "x" represents the unknown variable, while "a", "b", and "c" represent constants from the equation. Some common techniques used to solve linear equations include isolation, substitution, elimination, cross multiplication, and graphing.

When solving linear equations, there are several steps you must follow:

Isolate the variable: To do this, you need to get all the constants on one side of the equation and the unknown variable on the other side.
Combine like terms: This step is crucial when you have multiple terms on the same side of the equation. Combining like terms means adding or subtracting terms that have the same variables.
Use inverse operations: To undo the operations you performed on the other side of the equation, you use inverse operations. For example, if you subtracted a number, you would add its inverse to undo the subtraction.
Check your answer: After solving the equation, make sure to check your answer by plugging it back into the original equation. If the equation is true, your solution is correct.

Example:

Solve the equation 2x + 3 = 7 for x:

Isolate the variable: Subtract 3 from both sides of the equation: 2x + 3 - 3 = 7 - 3
Combine like terms: 2x = 4
Use inverse operations: Divide both sides of the equation by 2: 2x/2 = 4/2
Check your answer: x = 2

In conclusion, solving equations with one unknown is a fundamental skill in mathematics and various other disciplines. By understanding the basic principles and techniques, such as isolation, combination of like terms, and inverse operations, you can effectively solve linear equations and apply these concepts to more complex problems.