192CHAPTER12 First-Degree Equations in One Variable
Algebra involves the manipulation of equations or inequalities to find the values of variables,
also called unknowns. The simplest type of algebraic equation is called a first-degree equation
in one variable. That means there’s only one unknown to solve for, and it’s never raised to any
power (other than the first power).Constants, Sums, and Differences
Let’s explore what happens when we form equations by adding and subtracting variables and
constants on each side of an equality symbol.Letter constants
A constant can, and often does, take the form of a plain number. Then it appears in an
equation as a numeral. We might also see a constant symbolized by a letter such as a. The
actual value of a so-called letter constant might not be revealed, but we can always be sure
that it is fixed.
Letter constants can represent known irrational numbers when those numbers are
impossible to write in terms of numerals alone. We’ve already seen an example in this book:
π, the ratio of a circle’s circumference to its diameter. We can’t write out its exact value as a
numeral. Another well-known constant is an irrational number whose first few digits are
2.7182818 ..., and which is known as the exponential constant. This constant is symbolized
ase. Letter constants abound in physics and engineering. For example, c stands for the
speed of light in a vacuum, approximately 186,000 miles per second or 300,000 kilometers
per second.
When we see a letter constant in an equation, we must be sure that we know exactly what
it means. For example, e and c can represent general mathematical constants, having nothing
to do with exponentials or the speed of light. Here’s an example:ax+bx−cx−d=eCopyright © 2008 by The McGraw-Hill Companies, Inc. Click here for terms of use.