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One & Two Step Equations
Mathematics, Grade 6
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Study Guide One & Two Step Equations Mathematics, Grade 6
❮
1
/
3
❯
What
Is
Solving
and
Explaining
Two-Step
Equations
Involving
Whole
Numbers
and
Using
Inverse
Operations?
•
An
algebraic
equation
is
an
expression
in
which
a
letter
represents
an
unknown
number
such
as,
n
+
5
=
11
(n
=
6).
•
An
inverse
operation
is
one
that
“undoes”
or
reverses
another.
Addition
and
subtraction
are
inverse
operations,
and
so
are
multiplication
and
division.
•
Using
an
inverse
operation
allows
us
to
calculate
the
value
of
the
unknown
number
by
moving
all
the
known
numbers
to
one
side
of
the
equation.
•
Two-step
equations
involve
balancing
both
sides
of
the
equation.
To
solve
5
+
n
=
11,
subtract
5
(the
inverse
operation
of
addition)
from
both
sides:
n
=
11
–
5.
Perform
the
operation
and
n
=
6
How
to
solve
two-step
equations
involving
whole
numbers
by
using
inverse
operations:
•
To
solve
a
two-step
equation,
the
unknown
number
must
be
by
itself
on
one
side
of
the
equation.
This
happens
by
performing
inverse
operations.
•
An
algebraic
equation
must
stay
in
balance,
so
whatever
is
done
to
one
side
must
be
done
to
the
other.
To
solve
this
problem:
n
–
6
=
4
Add
6
to
both
sides
of
the
equation
because
addition
is
the
inverse
of
subtraction
n
=
10.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
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•
Just
as
addition
and
subtraction
are
inverse
operations,
so
are
multiplication
and
division.
To
solve
this
problem:
6n
=
30
Divide
both
sides
of
the
equation
by
6
because
division
is
the
inverse
of
multiplication
n
=
5.
•
When
solving
two-step
equations,
first
add
or
subtract
both
sides
using
the
inverse
operation
of
the
one
in
the
equation.
Addition
and
subtraction
are
ALWAYS
done
first.
2n
+
4
=
14
First
subtract
4
from
each
side
2n
=
10
Then
divide
each
side
by
2
n
=
5
•
Here
are
some
two-step
equations.
Notice
how
the
addition
or
subtraction
is
done
first
to
balance
the
equation.
The
inverse
operation
is
used
to
clear
the
addition
or
subtraction.
Then
an
inverse
operation
is
used
to
solve
the
problem
n/8
–
6
=
10
(add
6
to
both
sides)
n/8
=
16
(multiply
both
sides
by
8)
n
=
128
5n
+
5
=
20
(subtract
5
from
both
sides)
5n
=
15
(divide
both
sides
by
5)
n
=
3
© 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!
12n
–
5
=
31
______________________________________________
n/7
+
5
=
31
______________________________________________
9n
+
4
=
40
______________________________________________
n/6
–
18
=
2
______________________________________________
3n
–
14
=
16
______________________________________________
© 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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