Basic Mathematics for College Students

Evaluate Algebraic Expressions.

To evaluate an algebraic expression,we substitute given numbers for each variable
and perform the necessary calculations in the proper order.

4

8.1 The Language of Algebra 643

Self Check 6

ELECTIONSIn an election, the

incumbent received 55 fewer votes

than three times the challenger’s

votes. Let represent the number

of votes received by one

candidate. Write an expression

that represents the number of

votes received by the other.

Now TryProblem 91

x

SolutionRefer to the first drawing. If we let
the length of the handle (in inches), then
the length of the bristles is.
Now refer to the second drawing. If we
let the length of the bristles (in inches),
then the length of the handle is 10 b.

b 

10 h

h 

10 in.

h 10 – h

10 in.

10 – b b

EXAMPLE (^6) Enrollments Second
semester enrollment in a nursing program was 32
more than twice that of the first semester. Let
represent the enrollment for one of the semesters.
Write an expression that represents the
enrollment for the other semester.
StrategyThere are two unknowns: the
enrollment first semester and the enrollment
second semester. We will begin by letting the enrollment for the first semester.
WHYBecause the second-semester enrollment is related to the first-semester
enrollment.
Solution
Key phrase:more than Translation:addition
Key phrase:twice that Translation:multiplication by 2
The second semester enrollment was 2 x 32.
x
x
EXAMPLE (^7) Evaluate each expression for and :
a. b. c. d.
StrategyWe will replace each and in the expression with the given value of
the variable, and evaluate the expression using the order of operation rules.
WHYTo evaluate an expressionmeans to find its numerical value, once we know
the value of its variable(s).
Solution
a.
Evaluate each exponential expression.
 48 Do the addition.

 64  16

Substitute 4 for each y. We must write

4 within parentheses so that it is the

base of each exponential expression.

y^3 y^2 ( 4 )^3 ( 4 )^2

x y

y 0

x(1)

y^3 y^2 yx^05 xy^70

x 3 y 4

Self Check 7

Evaluate each expression for

and :

a.

b.

c.

Now TryProblems 73 and 85

a 2

b 3

a 2 ab

0 a^3 b^20

a 2 b 5

Somos/Veer

6

5

4

14

 16

48