evaluate

To evaluate an expression is to find the single number it comes out to. You take the general recipe, plug in specific values for its letters, and carry out the arithmetic until only a number remains. Evaluating 3x + 1 when x = 4 means computing 3·4 + 1 = 13.

Evaluation is substitution followed by arithmetic, and the arithmetic must obey the order of operations. After replacing the variables, you work through parentheses, then exponents, then multiplication and division, then addition and subtraction — left to right within each level. Skipping the order, for instance adding before multiplying, gives a wrong value.

Evaluating differs from solving. When you evaluate, the values of the variables are given to you and you compute the result; when you solve, the result is given and you hunt for the variable. Evaluation always produces an answer (provided no illegal step like dividing by zero appears); solving may produce one answer, many, or none.