Download Ch1-Section 1.4

§ 1.4
Introduction to Variable
Expressions and
Equations
Exponents
Exponential notation is used to write repeated
multiplication in a more compact form.
3333  3
4
34
exponent
base
The expression 34 is called an exponential expression.
Example: Evaluate 26.
2  2  2  2  2  2  2  64
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Martin-Gay, Beginning and Intermediate Algebra, 4ed
2
Order of Operations
Order of Operations
Simplify expressions using the order below. If grouping symbols
such as parentheses are present, simplify expressions within those
first, starting with the innermost set. If fraction bars are present,
simplify the numerator and the denominator separately.
1. Evaluate exponential expressions
2. Perform multiplication or division in order from left to right.
3. Perform addition or subtraction in order from left to right.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
3
Using the Order of Operations
Example:
6

9

3
Simplify the expression.
32
693
6

9

3

2
9
3
63

9
Simplify numerator and
denominator separately
Divide.

9
9
Add.

1
Simplify.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
4
Evaluating Algebraic Expressions
Definition
Variable: A symbol used to
represent a number.
Algebraic Expression: A
collection of numbers,
variables, operation symbols,
and grouping symbols.
Evaluating an Algebraic
Expression: Finding its
numerical value once we
know the values of the
variables.
Example
Evaluate: 7 + 3z when z = – 3
7  3z  7  3(3)
 7  (9)
 7 9
 2
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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Determining Whether a Number is a Solution
Definition
Equation: A mathematical
statement that two expressions
have equal value.
Example
5x = 10
4 + y = 2y – 5
Solving: In an equation
Solve the equation for a.
containing a variable, finding
x + 2 = 16
which values of the variable make
x = 14
the equation a true statement.
Solution: In an equation, a value
for the variable that makes the
equation a true statement.
Is –7 a solution of: a + 23 = –16?
a  23  16
(7)  23  16
– 7 is not a solution.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
6
Translating Phrases
Addition
(+)
Sum
Plus
Added to
More than
Increased
by
Total
Subtraction
(–)
Difference
Minus
Subtract
Less than
Decreased
by
Less
Multiplication
(·)
Product
Times
Multiply
Twice
Of
Division
()
Quotient
Divide
Into
Ratio
Divided
by
Martin-Gay, Beginning and Intermediate Algebra, 4ed
Equality (=)
Equals
Gives
Is/was/should
be
Yields
Amounts to
Represents
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Translating Phrases
Example:
Write as an algebraic expression. Let x to represent the unknown
number.
a.) 5 decreased by a number
b.) The quotient of a number and 12
a.) In words:
Translate:
5
5
decreased by
–
a number
x
The quotient of
b.) In words:
Translate:
a number
x
and

12
x
or
12
12
Martin-Gay, Beginning and Intermediate Algebra, 4ed
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