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INTRODUCTION TO ALGEBRA
COMMON MISTAKES
1
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Expressions vs. Equations
How to tell the difference
Expressions are a
combinations of term(s) (a
quantity expressed using
numbers and/or variables)
using the 4 basic operations
(+, -, x, or /)
Equations consist of
expressions using an “=“ to
set them equal to each
other. Equations can be
solved.


2
Complete Manual: ..\Introduction to Algebra Review.docx
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2 − 3 = 9x − x
− 1 = 8x
−1
=x
8
Common Mistakes

Incorrectly combining terms
when solving equations.

÷

Incorrect: x + 2 = 9 x + 3
is NO 10 x + 5 = 0 .
Correct x + 2 = 9 x + 3
becomes 2 − 3 = 9 x − x
− 1 = 8x
−1
=x
8
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Expressions – Evaluating
How to Evaluate
Expressions
To evaluate expressions,
substitute the values
where the variables occur.
After substituting the
given values into the
expression, apply the rules
for the Order of
Operations to correctly
simplify.


3
Complete Manual: ..\Introduction to Algebra Review.docx
To view; right click and open the hyperlink
Common Mistakes



Incorrectly applying the
Order of Operations to
simplify an expression.
Evaluate: − 3 x + 2 y − 1
if x = -2, y= -4
Incorrect: − 3 • −2 + 2 • −4 − 1
≠ −6 − 8 − 1
≠ −15

Correct:
− 3 • −2 + 2 • −4 − 1
= 6 + −8 − 1
= −3
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Combining Like Terms
How to combine like
terms


4
Common Mistakes
Like Terms are terms whose
variables have the same exponent
(also called the degree of the
term).


Not properly combining the Like
Terms.
2
2
+
+
−
Simplify: 2 x x 2 x x + 5
To combine like terms means to
simplify an expression by
combining the coefficients
(number or constant in front of
the variable) of like terms.

Incorrect: =(2 x −1x ) + (1x + 2 x ) + 5
Complete Manual: ..\Introduction to Algebra Review.docx
To view; right click and open the hyperlink
2
2
≠ 4x + 5
3

Correct:
=(2 x −1x ) + (1x + 2 x ) + 5
= x + 3x + 5
2
2
2
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