# Lesson 4: Equations and Their Solutions

Equations are mathematical statements that show that two expressions are equal. They are used to solve problems in math, science, engineering, and other areas. Equations can be written in many different forms, including linear equations, quadratic equations, and other forms. In this lesson, we will discuss equations and their solutions.

## Understanding Linear Equations Linear equations are equations of the form ax + b = c, where a, b, and c are constants and x is a variable. These equations can be solved by using the two-step process of isolating the variable, then solving for the value of the variable. In the equation ax + b = c, first isolate the variable by subtracting b from both sides of the equation, then divide both sides by a. This will give us the solution x = (c – b)/a. Quadratic equations are equations of the form ax2 + bx + c = 0, where a, b, and c are constants and x is a variable. These equations can be solved by using the quadratic formula, which is x = (-b ± √(b2 – 4ac))/2a. The quadratic formula can be used to solve equations with real or complex solutions. In the equation ax2 + bx + c = 0, first factor the equation if possible. If not, use the quadratic formula to find the solutions.

## Comparing to Other Equations Other equations, such as exponential equations and logarithmic equations, can also be solved using specific methods. Exponential equations can be solved using logarithms, while logarithmic equations can be solved using the change of base formula. Other equations, such as trigonometric equations and systems of equations, may require the use of more complex methods to find solutions.

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In this lesson, we discussed equations and their solutions. We discussed linear equations, quadratic equations, and other types of equations. We also discussed methods for solving these types of equations. Understanding equations and their solutions is an important part of mathematics, and is used in many areas of study. With the knowledge from this lesson, you should be able to solve a variety of equations.