Transcript Martin-Gay, Prealgebra, 6ed 7 7 - Mr. McCarthy

2.1 – 2.2
Introduction to
Variables, Algebraic
Expressions, and
Equations
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Algebraic Expressions
A combination of operations on letters (variables)
and numbers is called an algebraic expression.
Algebraic Expressions
5+x
6y
3y – 4 + x
4x means 4  x
and
xy means x  y
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Algebraic Expressions
Replacing a variable in an expression by a
number and then finding the value of the
expression is called evaluating the
expression for the variable.
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Evaluating Algebraic Expressions
Evaluate x + y for x = 5 and y = 2.
Replace x with 5 and y with 2 in x + y.
x+y=( 5) + ( 2)
=7
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Equation
Statements like 5 + 2 = 7 are called equations.
An equation is of the form expression = expression
An equation can be labeled as
Equal sign
x + 5 = 9
left side
right side
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Solutions
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.
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Solutions
Determine whether a number is a solution:
Is –2 a solution of the equation 2y + 1 = –3?
Replace y with –2 in the equation.
2y + 1 = –3
?
2(–2) + 1 = –3
?
–4 + 1 = –3
–3 = –3
True
Since –3 = –3 is a true statement, –2 is a solution of the equation.
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Solutions
Determine whether a number is a solution:
Is 6 a solution of the equation 5x – 1 = 30?
Replace x with 6 in the equation.
5x – 1 = 30
?
5(6) – 1 = 30
?
30 – 1 = 30
29 = 30
False
Since 29 = 30 is a false statement, 6 is not a solution of the
equation.
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Solutions
To solve an equation, we will use properties of
equality to write simpler equations, all equivalent to
the original equation, until the final equation has the
form
x = number or number = x
Equivalent equations have the same solution.
The word “number” above represents the solution of
the original equation.
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Keywords and Phrases
Keywords and phrases suggesting addition, subtraction,
multiplication, division or equals.
Addition
Subtraction
Multiplication
Division
Equal Sign
sum
difference
product
quotient
equals
plus
minus
times
into
gives
added to
less than
of
per
is/was/ will
be
more than
less
twice
divide
yields
total
decreased by
multiply
increased by
subtracted
from
double
divided by amounts to
is equal to
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Translating Word Phrases
the product of 5 and a number
5x
twice a number
2x
a number decreased by 3
n–3
a number increased by 2
z+2
four times a number
4w
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Additional Word Phrases
the sum of a number and 7
x+7
three times the sum of a number and 7
3(x + 7)
the quotient of 5 and a number
5
x
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Helpful Hint
Remember that order is important when subtracting.
Study the order of numbers and variables below.
Phrase
a number
decreased by 5
a number
subtracted from 5
Translation
x–5
5–x
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