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Introduction to Algebra
Mathematics, Grade 7
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Study Guide Introduction to Algebra Mathematics, Grade 7
❮
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3
❯
INTRODUCTION
TO
ALGEBRA
•
Algebra
is
the
practice
of
using
expressions
with
letters
or
variables
that
represent
numbers.
Words
can
be
changed
into
a
mathematical
expression
by
using
the
words,
plus,
exceeds,
diminished,
less,
times,
the
product,
divided,
the
quotient
and
many
more.
•
When
given
an
algebraic
expression,
it
can
be
solved
by
filling
in
a
number
for
the
variable.
•
Word
problems
can
be
turned
into
variable
expressions
by
changing
the
words
to
mathematical
terms.
•
If
an
expression
has
more
than
one
variable
expression,
it
can
be
combined
as
long
as
both
have
the
same
variable
factor;
this
is
called
combining
like
terms.
•
With
algebra,
inverse
operations
can
be
used
to
solve
equations.
Inverse
operations
are
used
to
isolate
a
variable.
Inverse
operations
undo
an
operation;
addition
is
the
inverse
operation
of
subtraction
and
vice
versa
as
well
as
multiplication
being
the
inverse
operation
of
division
and
vice
versa.
How
to
use
algebra:
•
An
example
of
an
algebraic
expression
is
3x
+
5.
Here
the
x
represents
a
number
that
is
to
be
multiplied
by
three.
If
x
=
2,
then
the
expression
equals
3
·
2
+
5
=
11.
By
filling
in
2
for
the
x,
the
expression
can
be
solved.
•
Words
can
be
changed
into
mathematical
terms.
Look
at
the
following
words
and
translate
them
into
mathematical
terms:
Ex.
Five
times
a
number
minus
three
→
5
·
n
-
3
=
5n
-
3
•
Each
word
represents
a
mathematical
term.
Once
this
is
done,
the
expression
can
either
be
left
this
way
or
solved
if
given
a
value
for
n.
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Permission
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for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
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www.NewPathLearning.com.
•
Word
problems
are
also
changed
into
variable
expressions
in
the
same
way.
Look
at
this
word
problem:
Jack
rented
a
movie.
The
store
charged
$1.99
for
the
first
day
and
$.50
for
each
day
after
that.
If
Jack
had
the
movie
for
d
days,
what
expression
could
be
used
to
represent
the
cost
of
renting
a
movie
in
terms
of
d?
$1.99
for
the
first
day
and
$.50
for
each
day
after
that
(.50
· d
)
→
the
expression
is
1.99
+
.50d
This
expression
can
be
solved
when
3
(or
any
other
number)
is
substituted
for
d,
the
number
of
days
Jack
had
the
movie.
So,
1.99
+
.50
· 3
=
1.99
+
1.50
=
3.49
or
$3.49.
•
If
an
expression
or
equation
has
more
than
one
variable
term,
the
terms
may
be
combined
if
the
terms
have
the
same
variable
factor.
Example:
5x
+
4
-
2x
→
3x
+
4
8x
-
6y
+
x
-
2y
→
9x
-
8y
•
To
solve
an
equation
using
inverse
operations,
the
variable
must
be
isolated
first
and
then
the
variable
can
be
solved.
Example:
Solve
for
x:
x
+
17
=
27
-
17
-17
x
=
10
Seventeen
is
subtracted
from
both
sides
to
solve
for
x.
On
the
left
side,
the
numbers
cancel
out
and
on
the
right
side
27
-
17
=
10,
the
answer.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
Try
This!
1.
Solve
if
n
=
3:
7
-
n
2n
+
8
4n
÷
6
2.
Translate
into
an
algebraic
expression:
o
Six
times
a
number
minus
two
o
A
number
plus
seven
3.
Translate
the
word
problem
into
a
variable
expression
in
terms
of
d,
days:
Sharon
rents
a
car
that
costs
$89
for
the
first
day
and
$50
for
every
day
after
that.
She
rents
the
car
for
d,
days.
4.
Combine
like
terms:
7x
-
4
x
11x
+
14y
-
5x
+
2y
6x
-
64
–
3x
5.
Solve
by
using
inverse
operations:
x
+
14
=
67
5x
=
45
x/2
=
42
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
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