Determine whether a mathematical problem contains an equal sign. If it does, as in 4x = 3, then it is an equation. If it doesn't, as in 4x - 3, then it is an expression.
Determine whether a written statement contains the words "is" or "equals." If it contains either of these words, it is a sentence, which can be translated into a mathematical equation. For instance, consider the statement "two is six less than a number." The presence of the verb "is" makes this a sentence, and it can therefore be written as an algebraic equation: 2 = n - 6, where the variable "n" is used to denote the unknown number. If a statement doesn't contain either "is" or "equals," then it is a phrase, not a sentence, and can be translated into a mathematical expression. For example, consider the statement "two less than the quantity 6 times a number." As this statement lacks a verb, it is merely a phrase, not a sentence, and therefore can be written as an algebraic expression. Using the variable "n" to denote the unknown number, the algebraic expression reads 6n - 2.
Understand the differences in working with each type of problem. A mathematical expression is defined as a succession of one or more terms that are separated by plus or minus signs, such as in 7x^2 - 5x + 4. Expressions can either be evaluated, producing a single number, or simplified, producing a shorter expression. For instance, a problem may read "evaluate 6t + 1 if t = -2." In this type of evaluation problem, substitute the given value for the variable. Here, replace "t," with "-2," yielding 6*-2 + 1. Perform calculations following the order of operations, yielding a solution of -11 in this case. Alternatively, you may be given a lengthier expression, such as 4v^2 - 8v + 1 + 5v^2 + 2v and asked to simplify it. Combine like terms by adding or subtracting them, in this case producing an answer of 9v^2 - 6v + 1. Equations set two expressions equal to one another, and unlike expressions, they can be solved. For instance, the equation 6a - 7 = 5 sets the expression "6a - 7" equal to the expression "5." Solve basic equations by first performing addition or subtraction and then performing multiplication or division. In the example, add 7 to both sides, obtaining 6a = 12, then divide both side by 6, yielding a solution of a = 2. More complex equations, such as b^2 + 3b - 4, may have two or more solutions, or no solution at all.