1
C H A P T E R 1
Review of Algebra
is book is a text on calculus, structured to prepare students for applying calculus to the physical
sciences. e first chapter has no calculus in it at all; it is here because many students manage to
get to the university or college level without adequate skill in algebra, trigonometry, or geometry.
We assume familiarity with the concept of variables like x and y that denote numbers whose
value is not known.
1.1 SOLVING EQUATIONS
An equation is an expression with an equals sign in it. For example:
x D 3
is a very simple equation. It tells us that the value of the variable x is the number 3. ere are a
number of rules we can use to manipulate equations. What these rules do is change an equation
into another equation that has the same meaning but a different form. e things we can do to
an equation without changing its meaning include the following.
• Add or subtract the same term from both sides. If that term is one that is already present
in the equation, we may call this
moving the term to the other side
. When this hap-
pens, the term changes sign, from positive to negative or negative to positive. For example:
x 4 D 5 is is the original equation
x D 5 C 4 Add 4 to both sides (move 4 to the other side)
x D 9 Finish the arithmetic
• Multiply or divide both sides by the same expression.