Easy Algebra Step-by-Step

66 Easy Algebra Step-by-Step

Solution

a. –5x

Step 1. Identify the numerical coeffi cient by observing that the number − 5

immediately precedes the variable x.

−5 is the numerical coeffi cient of x.

b. y

Step 1. Identify the numerical coeffi cient by observing that no number is

written immediately next to the variable y.

1 is the numerical coeffi cient of y.

c. πd

Step 1. Identify the numerical coeffi cient by observing that the number π

immediately precedes the variable d.

π is the numerical coeffi cient of d.

Evaluating Algebraic Expressions

Writing variables and coeffi cients or two or more variables (with or with-

out constants) side by side with no multiplication symbol in between is a

way to show multiplication. Thus, − 5 x means − 5 times x, and 2xyz means

2 times x times y times z. Also, a number or variable written immediately

next to a grouping symbol indicates multiplication. For instance, 6 ()x 1

means 6 times the quantity ()x+ , 7 x means 7 times x, and − 18 −

means − 1 times − 8.

An algebraic expression is a symbolic representation of a number. It can

contain constants, variables, and computation symbols. Here are examples

of algebraic expressions.

− 5 x, 2xyz,

6

71 x

()x 1

,

− ()−

+

15 +

1

y+ (^5) (
z

, −+ 8 −

5

2

xy^3227

x

, 8 ab^3336644 ,

xx^2 x− 12 ,

1

3

xz^232 , and − 25 xx^543 +++ 55 − 373 xx− 7 2 ++x 4

Ordinarily, you don’t know what number an algebraic expression repre-

sents because algebraic expressions always contain variables. However, if you

are given numerical values for the variables, you can evaluate the algebraic