Download 2.1 Notes Beginning Algebra

Chapter 2
Solving
Linear
Equations
and
Inequalities
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-1
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 the Variable on
Both Sides of the Equation
2.6 – Formulas
2.7 – Ratios and Proportions
2.8 – Inequalities in One Variable
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-2
Combining Like
Terms
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-3
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.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-4
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.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-5
Terms
The parts in an algebraic expression that
are added are called the terms of the
expression.
Expression
Terms
-2x + 3y - 8
-2x, 3y, -8
3y2 - 2x + 12
3y2, -2x, 12
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-6
Terms
The numerical part of a term is called its
numerical coefficient or coefficient.
Term
Numerical Coefficient
5x
5
7
1 x
2
4(x-3)
7
1
2
4
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-7
Like Terms
Like terms are terms that have the same
variables with the same exponents.
Like Terms
Unlike Terms
3x, -4x
3x, 2
4y, 6y
3x, 4y
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-8
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: 6.47b – 8.39b = -1.92b
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-9
Distributive Property
For any real numbers a, b, and c,
a(b + c) = ab + bc
Example: 2(x + 4) = 2x + 8
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-10
Simplifying an Expression
1.
2.
Use the distributive property to remove any
parentheses.
Combine like terms.
Example:
Simplify 6 + 2(4x + 9)
= 6 + 8x + 18
(Distributive Property)
= 8x + 24
(Combined Like Terms)
(Note: 8x + 24 is the same as 24 + 8x; however, we
generally write the term containing the variable first.
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-11