Download Chapter 2 Solving Linear Equations

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
2
Inequalities in
One Variable
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-3
3
Inequalities
An inequality is a mathematical statement
containing one or more inequality sign
(<, >, ,  ).
Inequalities
x + 3 < 14
x + 4  2x - 6
4 > -x + 3
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-4
4
Properties for Inequalities
For all real numbers a, b, and c:
1. If a > b, then a + c > b + c.
2. If a > b, then a - c > b – c.
3. If a > b and c > 0 then ac > bc.
b.

4. If a > b and c > 0 then a
c c
5. If a > b and c < 0 then ac < bc.
b.

6. If a > b and c < 0 then a
c c
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-5
5
Solving Inequalities
Example:
Solve the inequality and graph the solution.
x – 5 > -2
x – 5 + 5 > -2 + 5
(Add 5 to both sides)
x>3
-3
-2
-1
0
1
2
3
4
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-6
6
Solving Inequalities
Example:
Solve the inequality and graph the solution.
2x + 6 
–
2
2x + 6 - 6  – 2 – 6
2x  -8
(Subtract 6 from both sides)
(Divide both sides by 2)
x  -4
-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4
Copyright © 2015, 2011, 2007 Pearson Education, Inc.
Chapter 2-7
7