Variables are symbols, usually lowercase letters, that represent unknown numbers. For example, in the equation 4 + x = 6, "x" is a variable. In algebra, you often solve an equation to determine the value of a variable. Variables sometimes take letters that they represent, such as "s" for side, "t" for time or "d" for distance, but you can use any letter to represent a variable. Variables sometimes have numbers next to them, such as 3x or 4y, which indicate that the variable is multiplied by that number.
To solve an equation, follow the order of operations and always do the same thing to both sides. The order of operations refers to the steps and methods you use to solve an equation, such as addition and multiplication. When solving equations, simplify the parts in parentheses first, then exponents, then multiplication and division, and finally addition and subtraction. Remember this with the mnemonic: Please Excuse My Dear Aunt Sally. In addition, make sure you perform the same operations to each side. For example, to solve 4 + x = 6, you subtract 4 from both sides, leaving x = 2.
Algebra often involves graphing equations on a coordinate plane, which includes the x and y-axis. Looking at a graph helps you identify certain information about an equation. Linear equations, which form a line, usually take the form y = mx + b. This is called slope-intercept form, because it includes the slope or steepness, or "m" and the y-intercept, "b." You will also graph equations that do not form a straight line in later algebra classes, such as parabolas or exponential equations.
Algebra involves some new vocabulary. Some important terms include real numbers, which include all numbers that can be plotted on a graph; rational numbers, which can be made into a fraction; and irrational numbers, such as pi, which cannot be made into a fraction. Integers are whole numbers and can be negative or positive. A variable and its attached number, such as 3x, are considered a term. The number in front of the variable, such as 3 in 3x, is called the coefficient.