An equation is a mathematical statement that shows two expressions are equal. It contains an equals sign between the two expressions. For example, two plus three equals five, x plus four equals ten, and a squared plus b squared equals c squared. The equals sign is the key symbol that makes these mathematical statements into equations.
Every equation has two main parts: the left side, also called the left-hand side, and the right side, also called the right-hand side. These two parts are separated by the equals sign. An equation shows that both sides have the same value, creating a balance between the expressions.
There are different types of equations that serve various mathematical purposes. Simple equations involve basic arithmetic, like five plus three equals eight. Algebraic equations contain variables, such as x plus seven equals twelve. Linear equations have variables to the first power, like two x plus three equals nine. Quadratic equations contain variables squared, such as x squared plus four x equals five.
Solving an equation means finding the value that makes the equation true. Let's solve x plus three equals seven. Step one: subtract three from both sides to get x plus three minus three equals seven minus three. Step two: simplify to get x equals four. We can check our answer: four plus three equals seven, which is correct.
To summarize what we've learned about equations: An equation is a mathematical statement that shows two expressions are equal. It consists of a left side, an equals sign, and a right side. There are different types of equations that serve various mathematical purposes. Solving an equation means finding the value that makes the statement true. Equations are fundamental tools in mathematics for expressing relationships and solving problems.