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Algebraic Equations
Mathematics, Grade 6
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Study Guide Algebraic Equations Mathematics, Grade 6
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❯
ALGEBRAIC
EQUATIONS
What
are
algebraic
equations?
Algebraic
equations
are
mathematical
equations
that
contain
a
letter
or
variable,
which
represents
a
number.
To
solve
an
algebraic
equation,
inverse
operations
are
used.
Inverse
operations
are
performing
the
opposite
operation
to
what
is
being
performed
in
the
equation.
The
inverse
operation
of
addition
is
subtraction
and
the
inverse
operation
of
subtraction
is
addition.
Multiplication
and
division
are
the
inverse
operations
of
each
other.
There
are
different
types
of
algebraic
equations.
A
one-step
algebraic
equation
means
that
only
one
operation
needs
to
be
performed
in
order
to
solve
the
equation.
A
two-step
algebraic
equation
means
that
two
steps
are
needed
in
order
to
solve
the
equation.
Another
algebraic
equation
that
is
commonly
used
is
the
Interest
equation,
I
=
P
·
r
·
t.
This
equation
is
used
to
find
simple
interest,
I,
given
the
principle,
P,
the
rate,
r,
and
the
time,
t.
When
three
of
the
four
numbers
are
given,
the
fourth
can
be
found
using
a
two-step
algebra.
How
to
use
algebraic
equations:
•
Algebraic
equations
are
solved
using
the
inverse
operations.
To
solve
the
equation
n
-
52
=
38,
look
to
see
what
operation
is
being
performed
in
the
problem,
subtraction.
The
inverse
operation
of
subtraction
is
addition.
The
problem
can
be
solved
using
the
inverse
operation
of
addition
as
the
example
shows:
n
-
52
=
38
+
52
+52
n
=
90
Since
52
was
subtracted
in
the
initial
problem,
it
will
be
added
with
inverse
operations.
The
rule
when
dealing
with
equations
is
whatever
is
done
to
one
side
of
the
equation
must
be
done
to
the
other
side.
So
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Permission
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purchaser
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Visit
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52
is
added
to
38
on
the
other
side
of
the
equal
sign.
When
both
sides
are
added,
the
52's
on
the
left
side
of
the
equation
cancel
out,
leaving
only
the
n.
On
the
right
side
of
the
equation,
38
and
52
are
added,
giving
the
answer
of
90.
Therefore
n
=
90.
This
is
a
one-step
equation.
•
Look
at
the
two-step
equation
below
and
how
to
solve
it.
3n
+
12
=
27
-
12
-12
3n
=
15
3
3
n
=
5
In
this
equation,
12
is
subtracted
first
from
both
sides.
This
because
the
variable
needs
to
be
alone
before
it
can
be
solved.
Now
the
equation
is
3n
=
15.
Since
the
3
is
multiplied
by
n,
division
must
be
used
in
order
to
solve
for
n.
When
3
is
divided
by
both
sides,
the
result
is
n
=
5.
T
•
The
interest
equation,
I
=
P·r·t,
is
also
a
two-step
equation.
When
given
the
principle,
rate
and
interest,
multiplication
is
used
to
solve
for
the
interest.
If
interest
is
given,
along
with
two
others,
use
inverse
operations
to
solve.
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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
the
following:
n
-
4
=
16
56
+
n
=
134
n
+
98
=
207
2n
-
6
=
12
4n
-
36
=
144
5n
+
75
=
110
2.
Solve
for
I,
I
=
P·r·t:
P
=
$1000,
r
=
8%,
t
=
2
years
P
=
$5000,
r
=
4%,
t
=
1
year
3.
Solve
for
the
missing
variable,
I
=
P·r·t:
I
=
$500,
r
=
8%,
t
=
2
years
I
=
$50,
P
=
$2000,
t
=
1
year
© 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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