ALGEBRA EXPLAINED
What is an expressionin mathematics?
An expression in mathematics is a statement that uses either numbers, variables, or
both. For example, the following are all mathematical expressions:
y
4
6 4
5 x 7
4 5 (3 2)
x 4 (7 x)
In order to write an expression from a written mathematical problem, one has to
interpret the text. For example, if one person weighs 100 pounds and another weighs y
pounds; the expression for their combined weights would be 100 y.
What are equations?
In its simplest form, an equation is represented by expressions written with an equal
sign in between; the two entities on either side are equal to each other. They are
among the simplest mathematical problems most people deal with (most people have
solved equations in their daily lives without realizing it). For example, when students
first learn addition in school, they typically work on equations such as: ___ 5 7,
in which the blank needs to be filled. This problem could also be expressed as x 5
7, a simple equation. In this case, the equation is solved when xequals 2. The follow-
ing are also equations:
6 6
x 8
y 8 14
x 4 15 x
5 xy 8 xy^2 4
There are also some fundamental properties of equations that are good to know.
They include symmetric properties (if ab,then ba); substitution (if ab,then
amay be replaced by b); addition (if ab,and cis a number, then acbc);
and multiplication (if ab,and cis a number, then acbc).
What are algebraic equations?
An algebraic equation,as with the equations defined above, is a statement in which two
numbers, letters, or expressions are equal. But algebraic equations take this idea even
further: Most of the time, the objective is to try to simplify the numbers and the one (or 133