Solving Equations

Chapter: Solving Equations

  • Definition of an Equation: An equation is a mathematical sentence that shows the relationship between two expressions, often symbolized with an equals sign (=).

  • Value of the Variable: In an equation, there is typically one or more variables. The purpose of solving the equation is to find the values of these variables that makes the equation true.

  • Balancing the Equation: When you solve an equation, you must maintain a balance between both sides. Any operation performed on one side must be applied to the other.

  • Solving for One Variable: If there is only one variable, it’s simply a matter of isolating the variable on one side and a number on the other. This is typically done by adding, subtracting, multiplying, or dividing both sides by the same value.

  • Solving for Multiple Variables: If there are multiple variables, it’s a more complex process. You usually need more than one equation to find the values of the variables.

  • Using Addition and Subtraction: If an equation has a number added or subtracted from the variable, you can isolate the variable by doing the opposite - subtracting or adding the same amount from both sides.

  • Using Multiplication and Division: If an equation has a number multiplied or divided by the variable, you can isolate the variable by doing the opposite - dividing or multiplying both sides.

  • Dealing with Exponents: If a variable is raised to a power, the opposite operation is taking the root of both sides. If the power is 2, square root is used; if the power is 3, cube root is used, and so on.

  • Solving Quadratic Equations: Quadratic equations, ones which involve variables to the power of 2, can be solved by factoring, completing the square, or using the quadratic formula.

  • Checking Solutions: After you find a potential solution for an equation, you should check your answer. Substitute your solution back into the original equation to ensure it makes both sides equal.

Remember, consistent practice is key to mastering the art of solving equations. Make sure to utilize past papers and online resources to strengthen your understanding.