The Handy Math Answer Book

then add x^2 to each side (another way of subtracting): 2x 9  2 x 4

then add 2xto each side: 4x 9  4

then add 9 to each side: 4x 5

then multiply each side by 1/4 (divide by 4): x5/4

What are functions?

Functions are mathematical expressions describing the relationship between variables

and involve only algebraic operations. If there is one independent variable, the depen-

dent variable, for example y, can be determined through the function. This is often

seen written as yf(x), spoken as “y equals f of x” (functions also use notation with x;

for example, f(x)  2 x1 is a function). Functions within equations are also com-

mon; for example, in the equation x^2 y3, the yrepresents a function of x. This

equation can also be written as y 3 x^2.

Functions do not always have to be in terms of f(x). They can just as easily be

termed g(x), depending on the equation. But note: The equation x^2 y^2 9 is nota

function, as xand yare both independent variables.

What is a coefficient?
In an algebraic equation, a coefficient is simply a multiplicative factor. In the majority
of cases, the coefficient is the numerical part (most often a constant) of the equation.
138 Thus, it is called a numerical coefficient. For example, in 3x6, the coefficient is 3;

What is the order of operations

when one simplifies an algebraic equation?

T

here is a certain order to working out an algebraic equation. The following

lists the operations in their correct order:

1. Do what is inside the parentheses


2. Do the exponents


3. Do all the multiplications and divisions from left to right


4. Do all the additions and subtractions from left to right
   There are also rules when it comes to grouping in algebraic equations, espe-
   cially when working with parentheses. When an expression has parentheses
   within parentheses, work from the inside out, removing the innermost paren-
   theses first. And remember, if there is a positive sign in front of the parentheses,
   it does not change any sign inside the parentheses; if there is a negative sign in
   front of the parentheses, it willchange all the signs within the parentheses.