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# Basic Algebra : sub-module 3 of 4 of math tutorials

You have likely worked with linear equations if, for example, you have ever calculated your salary based on an hourly wage, or compared the costs of cell phone plans. The applications of solving linear equations are widespread and appear in several fields and careers. Solving an algebraic equation is like solving a puzzle, where the solution is the value of the variable that makes the equation true. This module will introduce you to the basic concepts of solving equations, help you solve single-step and multi-step linear equations, as well as show you how to rearrange equations to isolate for a given variable.

## Top Tips

• Know your algebra terminology. For example, a variable is an unknown number that is usually represented by a letter. Understanding the words commonly used in algebra will help you solve problems.
• To solve an equation, get the variable all by itself on one side of the equation. Solving an equation means finding the value of the variable that makes the equation a true statement. If the variable is by itself, everything else on the other side of the equation must be equal to the variable.
• To solve an equation, perform the usual order of operations in reverse to isolate for the variable. We “undo” each operation by performing the inverse operation to both sides of the equation until we have the variable alone on one side of the equation.
• Get comfortable working with fractions and negative numbers. These will appear often and you need to be able to work with them.
• Make sure to keep your equation in balance. What you do to one side of the equation you must also do to the other side of the equation. For example, if you add 3 to the right side of the equation, you must also add 3 to the left side of the equation to keep the equation balanced.
• Look to see if an equation can be simplified before you start to solve it. This may include things like collecting like terms or expanding brackets so that your equation is easier to work with.
• Always check your answer. Substitute the solution into the given equation and verify that the left side of the equation equals the right side of the equation.