Download Chapter 2 Solving Linear Equations

Chapter 2
Solving
Linear
Equations
and
Inequalities
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-1
2-1
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
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-2
2-2
2
The Addition
Property of
Equality
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-3
2-3
3
Linear Equations
A linear equation in one variable is an
equation that can be written in the form
ax + b = c where a, b, and c are real
numbers and a  0.
The solution to an equation is the number
that when substituted for the variable makes
the equation a true statement.
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-4
2-4
4
Solutions to Equations
Example:
Consider the equation 2x – 4 = 6. Determine whether
-3 is a solution.
x = -3
2x – 4 = 6
?
2(-3) – 4 = 6
?
-6 – 4 = 6
-10 = 6
(False)
Since we obtained a false statement, x = -3 is not a
solution to the equation.
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-5
2-5
5
Equivalent Equations
Two or more equations with the same
solution are called equivalent equations.
We ensure that an equation always remains
balanced by doing the same thing to both sides of
the equation.
Left side
=
Right side
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-6
2-6
6
Addition Property of Equality
If a = b, then a + c = b + c for any
real numbers a, b, and c.
Example:
Solve the equation x – 4 = - 3
x – 4 = -3
x – 4 + 4 = -3 +4 (Add 4 to both sides.)
x+0=1
x=1
Check:
x – 4 = -3
1 – 4 = -3
-3 = -3 (True)
Copyright
© 2011,
2015, 2007
2011,Pearson
2007 Pearson
Education,
Copyright
© 2015,
Education,
Inc. Inc.
Chapter
Chapter1-7
2-7
7