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Algebraic Expression
• Can have variables, numbers, addition,
subtraction, multiplication, division, parenthesis,
square roots, exponents…
• Examples:
x2
3  x  2
5b  7c  d
5 xy
Variable
• Symbols or letters used to represent an
unknown
• Examples:
x



Term
• How many items are being added, subtracted,
divided
• Examples:
2
5a  2 xy  3
3
P  2x
2
a b
4
Like Terms
• Same variable raised to the same power
• Examples:
2
2
5 x y and 8 x y
2
7y and 22y
2
Coefficient
• The number in front of a variable
• Examples:
123 xy
3 2
123
9xy z
9
x
1
Exponent
• The number up in the air next to a base
• The number of times you multiply something
times itself
• Examples:
3
3
12
12
2
x
4
3 y  7
4
Base
• What the exponent sits on
• The part that has been raised to a power
• Examples:
3
2
12
x
2
x
4
3 y  7
y
Constant
• A number that has no variable
• It can be positive or negative
• Examples:
42
-42
3x  5
5
2
4
5 x  3y  8
-8
IXL
• https://www.ixl.com/math/grade-8/identify-terms-andcoefficients
Properties of Equality
•Properties are rules that
allow you to balance,
manipulate, and solve
equations
Addition Property of
Equality
•Adding the same number to both
sides of an equation does not
change the equality of the
equation.
•If a = b, then a + c = b + c.
•Ex: x=y, so x+2=y+2
Subtraction Property of
Equality
•Subtracting the same number to
both sides of an equation does not
change the equality of the
equation.
•If a = b, then a – c = b – c.
•Ex: x = y, so x – 4 = y – 4
Multiplication Property of
Equality
•Multiplying both sides of the
equation by the same number,
other than 0, does not change the
equality of the equation.
•If a = b, then ac = bc.
•Ex: x = y, so 3x = 3y
Division Property of
Equality
•Dividing both sides of the equation
by the same number, other than 0,
does not change the equality of
the equation.
•If a = b, then a/c = b/c.
•Ex: x = y, so x/7 = y/7
Symmetric Property of
Equality
•If numbers are equal, they will still
be equal if the order is changed.
•If a = b, then b = a.
•Ex: x = 4, then 4 = x
Why Do We Need Properties
• We need it to solve and manipulate equations.
• It is imperative for students to be fluent in manipulating
equations in this class.
• Fluency = Speed + Accurate
Example 1
• 2(x – 5) = 8x + 2
Original
2x – 10 = 8x + 2
Distribute Property
-6x – 10 = 2
Subtraction property of Equality
-6x = 12
Addition Property of Equality
x = -2
Division Property of Equality
Solving for x Challenge