Download Evaluating Algebraic Expressions Identifying

Math 64
1.8 "Introduction to Variables, Algebraic Expressions, and Equations"
Objectives:
*
Evaluate algebraic expressions given replacement values.
*
Identify solutions of equations.
*
Translate phrases into variable expressions.
Evaluating Algebraic Expressions
Perhaps the most important quality of mathematics is that it is a science of patterns. Communicating about patterns
is often made easier by using a letter to represent all the numbers …tting a pattern. We call such a letter a variable. Using
variable notation is a primary goal of learning algebra.
We now take some important …rst steps in beginning to use variable notation. A combination of operations on letter (variables) and numbers is called an algebraic expression or simply an expression.
:
Replacing a variable in an expression by a number and then …nding the value of the expression is called evaluating the
expression for the variable. When …nding the value of an expression, remember to follow the order of operations.
Example 1: (Evaluating algebraic expressions)
Evaluate each expression for x = 2; y = 5; and z = 3:
a) x5 + (y
c) xy (5 + z
z)
x)
b) z
d)
x + 2y
7x + 2y
3x
Identifying Solutions of Equations
When an equation contains a variable, deciding which values of the variable make an equation a true statement is called
solving an equation for the variable. A solution of an equation is a value for the variable that makes an equation a true
statement.
Page: 1
Notes by Bibiana Lopez
Prealgebra by Elayn Martin-Gay
1.8
Example 2: (Identifying solutions of equations)
Determine which numbers in each set are solutions to the corresponding equations.
a) 3 (n
4) = 10;
f5; 7; 10g
b) 9x
15 = 5x + 1;
f2; 4; 11g
Translating Phrases into Variable Expressions
To aid us in solving problems later, we practice translating verbal phrases into algebraic expressions. Certain key words
and phrases suggesting addition, subtraction, multiplication, or division are reviewed next.
Key Words That Indicate Operations:
Addition (+) Subtraction ( ) Multiplication ( )
Division ( )
sum
di¤erence
product
quotient
plus
minus
times
divide
added to
subtract
multiply
shared equally among
more than
less than
multiply by
per
increased by
decreased by
of
divided by
total
less
double/triple
divided into
Example 3: (Translating phrases into variable expressions)
Write as an algebraic expression. Use x to represent "a number."
a) Twice a number.
b) 8 increased by a number.
c) 6 less than three times a number.
d) Seven times the sum of a number and 2.
e) 5 divided by a number plus 3.
f) The product of a number and 3 increased by 1.
Page: 2
Notes by Bibiana Lopez