This chapter covers solving for unknowns using linear equations.
SOLVE for the unknown given a linear equation.
The rules for addition, subtraction, multiplication, and division described in previous lessons will
apply when solving linear equations. Before continuing this course it may be worthwhile to
review the basic math laws in Module 1 and the first chapter of this module.
Solutions to Algebraic Equations
The equation is the most important concept in mathematics. Alone, algebraic operations are of
little practical value. Only when these operations are coupled with algebraic equations can
algebra be applied to solve practical problems.
An equation is a statement of equality between two equal quantities. Most people are familiar
with the concept of equality. The idea of equal physical quantities is encountered routinely. An
equation is merely the statement of this equality. There are three key ideas in an equation: an
equation must involve two expressions, the expressions must be equal, and the equation must
indicate that the expressions are equal. Thus, the statement that the sum of three and one equals
four is an equation. It involves two expressions, (four and the sum of three and one), the
expressions are equal, and the equation states that they are equal.
The equal sign (=) is used to indicate equality in an equation. In its most general form, an
algebraic equation consists of two algebraic expressions separated by an equal sign. The equal
sign is the key sign in algebra. It is the sign that defines one expression in terms of another.
In solving practical problems, it is the sign that defines the unknown quantity in terms of known
There are two kinds of equations: identities and conditional equations. An identity is an equation
that is true for all values of the unknown involved. The identity sign () is used in place of the
equal sign to indicate an identity. Thus, x2 (x)(x), 3y + 5y 8y, and yx + yz y(x + z) are all
identities because they are true for all values of x, y, or z. A conditional equation is one that is
true only for some particular value(s) of the literal number(s) involved. A conditional equation
is 3x + 5 = 8, because only the value x = 1 satisfies the equation. When the word equation is
used by itself, it usually means a conditional equation.