Membership
Sign Up
Sign In
Can't access your account?
Explore Curriculum
Research
Standards Correlations
Teacher Reviews
Science
Math
Social Studies
READING/ELA
Sign in
MEMBERSHIP
Explore Curriculum
Research
Standards Correlations
Teacher Reviews
Back
Equations and Inequalities
Mathematics, Grade 7
Back
Study Guide
Provides a quick overview of the topic selected!
Flash Cards
Practice and review the topic selected with illustrated flash cards!
Quiz
Assess students’ understanding of the topic selected!
Worksheets
Print illustrated worksheets!
Games
Engage students with interactive games.
Study Guide Equations and Inequalities Mathematics, Grade 7
❮
1
/
3
❯
EQUATIONS
AND
INEQUALITIES
•
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.
•
Inequalities
are
mathematical
equations
that
compare
two
quantities
using
greater
than,
>;
greater
than
or
equal
to
≥;
less
than,
<; a
nd
less
than
or
equal
to,
≤.
Inequalities
are
also
solved
by
using
inverse
operations.
•
Often
a
number
line
is
used
to
show
inequalities.
To
show
an
inequality
on
the
number
line,
a
shaded
circle
is
used
to
represent
that
the
answer
is
equal
to
a
number.
A
non-shaded
circle
means
the
answer
is
not
equal
to
a
number.
A
shaded
arrow
on
the
number
line
to
the
left
of
a
circle
means
that
the
answer
is
less
than
the
circled
number.
If
the
shaded
arrow
is
to
the
right,
the
answer
is
greater
than
the
circled
number.
How
to
use
equations
and
inequalities:
•
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.
© 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.
•
The
rule
when
dealing
with
equations
is
whatever
is
done
to
one
side
of
the
equation
must
be
done
to
the
other
side.
So
52
is
added
to
38
on
the
other
side
of
the
equal
sign.
When
both
sides
are
added,
the
numbers
on
the
left
side
of
the
equation
will
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.
•
Inequalities
are
solved
the
same
way
as
algebraic
equations
by
using
inverse
operations.
The
only
rule
of
inequalities
that
must
be
remembered
is
that
when
a
variable
is
multiplied
or
divided
by
a
negative
number
the
sign
is
reversed.
Ex.
x
+
3
≥
7
-2x
< 28
-
3
-3
-2
-2
x
≥
4
x
>
-14
(Notice
sign
is
reversed)
The
result
is
x
≥
4.
This
means
that
x
can
be
any
number
that
meets
this
requirement
such
as
4,
8,
10,
20
etc.
•
On
the
number
line
the
answer
would
look
as
follows:
•
The
inequality
x
<
2
on
the
number
line
would
look
as
follows:
•
To
write
an
inequality,
translate
the
words
into
numbers
and
signs:
greater
than
>
greater
than
or
equal
to
≥
less
than
<
less
than
or
equal
to
≤
© 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!
Solve
the
following
equations:
x
-
4
=
16
56
+
x
=
134
6x
=
84
x/7
=
15
Solve
and
graph
the
following
inequalities:
x
+
14
≤
35
x
-
12
>
42
4x
<
128
x/-2
≥
18
Write
the
following
inequalities:
© 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.
Need Help?
Contact Us
Browse Virtual Catalog
Request a Catalog
Order Form
W-9 Form
FAQs
NewPath Learning
About Us
Our Team
Awards & Endorsements
Grants & Funding
Product Suggestions
Custom Publishing
Collaborate Online
Our Blog
Solutions
Review & Reinforcement
Intervention & Enrichment
Test Prep
After School/Summer School
Parental Involvement
Professional Development
Shop By Product
Curriculum Mastery Games
Flip Charts
Visual Learning Guides
Curriculum Learning Modules
E-Books/Workbooks
Posters & Charts
Study/Vocabulary Cards
Digital Curriculum
Online Learning
Online Printable Worksheets
Shop By Grade
Early Childhood
First Grade
Second Grade
Third Grade
Fourth Grade
Fifth Grade
Sixth Grade
Seventh Grade
Eighth Grade
High School
Shop By Subject
Science
Math
Reading/ELA
ESL & Spanish
Social Studies
Health
© 2021 NewPath Learning all right reserved
|
Privacy Statements
|
Term of use
|
Website design WinMix Soft