Download Combining Like Terms

Chapter 2
Solving Linear
Equations and
Inequalities
Chapter Sections
2.1 – Combining Like Terms
2.2 – The Addition Property of Equality
2.3 – The Multiplication Property of Equality
2.4 – Solving Linear Equations with a Variable on One
Side of the Equation
2.5 – Solving Linear Equations with a Variable on Both
Sides of the Equation
2.6 – Formulas
2.7 – Ratios and Proportions
2.8 – Inequalities in One Variable
Angel, Elementary Algebra, 7ed
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Adding with Same Signs
To add real numbers with the same sign,
add their absolute values. The sum has the
same sign as the numbers being added.
Example:
–12 + (–3) = –9
5 + 29 = 34
The sum of two positive numbers will
always be positive and the sum of two
negative numbers will always be negative.
Angel, Elementary Algebra, 7ed
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Adding with Different Signs
To add real numbers with the different
signs, subtract the smaller absolute value from
the larger absolute value. The sum has the sign
of the number with the larger absolute value.
Example:
12 + (–3) = 9
–28 + 32 = 4
The sum of two numbers with different
signs may be positive or negative. The sign
of the sum will be the same as the sign of the
number with the larger absolute value.
Angel, Elementary Algebra, 7ed
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§ 2.1
Combining Like
Terms
Terms
The parts in an algebraic expression that
are added are called the terms of the
expression.
Expression
Terms
-3x + 8y - 15
1
2
6w + 12z - 3
-3x, 8y, -15
6w2,
Angel, Elementary Algebra, 7ed
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12z, - 3
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Terms
The numerical part of a term is the
numerical coefficient or coefficient.
Term
Coefficient
-3x
-3
8y
x
3
8
6w2
1 , since 1x means 1 x
3
3
3
6
Angel, Elementary Algebra, 7ed
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Like Terms
Like terms are terms that have the same
variables with the same exponents.
Like Terms
1
-3x, 8x, - 3 x
6w2, -12w2, w2
Unlike Terms
20x, x2, x3
6xy, 2xyz, w2
Angel, Elementary Algebra, 7ed
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Combining Like Terms
1. Determine which terms are like terms.
2. Add or subtract the coefficients of the like
terms.
3. Multiply the number found in step 2 by the
common variable(s).
Example: 5a + 7a = 12a
Angel, Elementary Algebra, 7ed
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Distributive Property
For any real numbers a, b, and c,
a(b + c) = ab + bc
Example: 3(x + 5) = 3x + 15
(This is not equal to 18x! These are
not like terms.)
Angel, Elementary Algebra, 7ed
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Simplifying an Expression
1.
2.
Use the distributive property to remove any
parentheses.
Combine like terms.
Example:
Simplify 3(x + y) + 2y
= 3x + 3y + 2y
(Distributive Property)
= 3x + 5y
(Combine Like Terms)
(Remember that 3x + 5y cannot be combined because they
are not like terms.)
Angel, Elementary Algebra, 7ed
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