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Algebraic Equations
Mathematics, Grade 7
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Study Guide Algebraic Equations Mathematics, Grade 7
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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.
When
algebraic
equations
are
written
in
words,
the
words
must
be
changed
into
the
appropriate
numbers
and
variable
in
order
to
solve.
To
solve
an
algebraic
equation,
inverse
operations
are
used.
Two-step
equations
involve
two
different
mathematical
operations
that
must
be
evaluated
in
order
to
solve
the
equation.
Equations
can
be
solved
using
addition,
subtraction,
multiplication
and
division.
Most
two-step
equations
involve
either
addition
or
subtraction
with
either
multiplication
or
division.
Some
algebraic
equations
can
contain
variables
on
both
sides
of
an
equation.
In
this
case,
the
variables
and
numbers
need
to
be
moved
so
there
are
only
variables
on
one
side
and
numbers
on
the
other
side
before
evaluating.
How
to
use
algebraic
equations
Algebraic
equations
written
as
words
or
word
problems
must
be
changed
into
the
correct
numbers
or
variables
before
solving.
For
example,
what
is
the
phrase,
five
times
a
number
decreased
by
four
is
sixty-three,
as
a
mathematical
equation?
Ex.
Five
times
a
number
→
5x
decreased
by
four
→
-4
is
sixty-three
→
=
63
The
equation
is
5x
-
4
=
63.
Once
the
words
or
word
problems
have
been
changed
to
numbers,
the
equation
can
be
evaluated.
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Permission
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granted
for
the
purchaser
to
print
copies
for
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educational
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To
evaluate
two-step
equations,
inverse
operations
are
used.
With
two-step
equations,
it
is
very
important
to
isolate
the
variable
before
evaluating.
Isolating
the
variable
means
to
get
the
variable
alone
on
one
side
of
the
equation.
For
example,
evaluate
3x
+
2
=
23.
Ex.
3x
+
2
=
23
→
isolate
the
variable
by
subtracting
2
-
2
-2
3x
=
21
→
now
solve
for
x
3
3
x
=
7
In
this
equation,
x
=
7.
If
3
was
divided
first
and
then
2
was
subtracted,
the
result
would
be
incorrect.
Algebraic
equations
can
also
have
variables
on
both
sides
of
the
equal
sign.
To
solve
for
these
equations,
the
variables
must
be
on
one
side
of
the
equal
sign
and
the
numbers
must
be
on
the
other
side
of
the
equal
sign.
Then
the
equation
can
be
evaluated.
For
example,
solve
for
3x
-
3
=
x
+
7.
Ex.
First
move
the
numbers
over
→
3x
-
3
=
x
+
7
+3
+3
The
equation
now
becomes
→
3x
=
x
+
10
Now
move
the
variable
over
→
-x
-x
2x
=
10
x
=
10/2
=
5
The
answer
for
this
equation
is
5.
Answers
of
algebraic
equations
should
be
checked
by
plugging
the
answer
for
x
in
the
original
equation.
In
this
case,
(3)(5)
-3
=
5
+
7
or
15
-
3
=
12
or
12
=
12.
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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.
What
is
the
algebraic
equation
that
means
a
number
divided
by
four
plus
two
is
six?
2.
Solve
for
x,
3x
-
7
=
5
3.
Solve
for
x,
x/6
+
21
=
27
4.
Solve
for
x,
9
-
5x
=
-31
5.
Solve
for
x,
12
+
x
=
6
+
3x
6.
Solve
for
x,
3x/4
=
8
+
x
© 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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