LINEAR EQUATIONS AND THEIR
GRAPHES
COMMON MISTAKES
1
10/20/2009
Linear Equations-Addition/Subtracting
How to Add/Subtract
Linear Equations


2
Correctly get variables on
one side of the ‘=‘ sign and
constants (numbers) on the
other side by applying the
Order of Operations in
reverse.
To Reverse of the Order of
Operations is to FIRST + or –
the constant (whichever is
OPPOSITE of the operation in
the expression) from both
sides.
Complete Manual:..\Linear Equation Review.docx
To view; right click the open the hyper link
Common Mistakes



Not correctly reversing the
Order of Operations.
x + 16 = −4
Solve:
Incorrect:
+ 16 + 16
x ≠ 12

Correct:
x + 16 = −4
− 16 − 16
x = −20
10/20/2009
Linear Equations-Multiplying/Dividing
How to Multiply/Divide
Linear Equations


3
Correctly get variables on
one side of the ‘=‘ sign and
constants (numbers) on
the other side by applying
the Order of Operations in
reverse.
Reverse of the Order of
Operations is to FIRST x
or /(whichever is opposite of
the operation in the
expression) to both sides.
Complete Manual:..\Linear Equation Review.docx
To view; right click the open the hyper link
Common Mistakes



Not correctly reversing the
Order of Operations.
Solve:
3x = −96
Incorrect: − 3
−3
x ≠ −99

Correct:
3x = −96
3
3
x = −32
10/20/2009
Two-Step Equations - Solving
How to Solve Two-Step
Equations


Step 1: Correctly get variables
on one side of the ‘=‘ sign and
constants (numbers) on the
other side by applying the
Order of Operations in
reverse.
Step 2: Solve the equation for
the variable by applying the
Order of Operations in
reverse to the coefficient of
the variable and the constant
on the other side of the ‘=‘.
Common Mistakes

Not correctly reversing the Order of
Operations.

Solve:

Incorrect: + x
x + 16 = 3 x − 4
x + 16 = 3 x − 4
+x
16 = 4 x − 4
+4
+4
20 = 4 x
5≠ x

Correct:
x + 16 = −3 xx − 4
−x
16 = 2 x − 4
+4
20 = 2 x
10 = x
4
Complete Manual:..\Linear Equation Review.docx
To view; right click the open the hyper link
10/20/2009
+4
Equations with Parentheses
How to read Parentheses


5
Common Mistakes
Parentheses ( ) are used to
“group” terms so as to
consider the “stuff” inside as
one term.

When applying the Order of
Operations, the ( ) are to be
considered the first quantity
with which to operate on.

Complete Manual:..\Linear Equation Review.docx
To view; right click the open the hyper link

Not properly applying the Order
of Operations or the Distributive
Property.
− (x − 3x +1 )
Incorrect:
≠ − x − 3x +1
2
2
Correct:
− (x − 3x +1 )
2
= − x + 3x −1
2
Since “ –( “ really means −1 •(…
and that tells you to multiply
each term by −1 .
10/20/2009
Distributive Property-Applying It
How to Correctly Apply
the Distributive Property
The Distributive Property is
defined to be…
a(x +c) = ax +ac.
It is said to use multiplication
over addition.
Confusion results when a =-1
because then it is written as
-(x + c) but is really -1(x + c)
and that is = –x - c.



6
Complete Manual:..\Linear Equation Review.docx
To view; right click the open the hyper link
Common Mistakes

Only applying the Distribution
Property to part of the expression
 Incorrect: − 2( x + 9) ≠ −2 x + 2 • 9
≠ −2 x + 18

Correct:
− 2(x + 9) = −2x + −2 • 9
= −2x − 18
Note: The expression can include
several terms, but the process is
still the same: every term is
multiplied by the number (the
constant) outside the
parentheses.
10/20/2009