Chapter 2

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 1-11

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-1

Solving Linear Equations and Inequalities

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-2

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 Only 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

Chapter Sections

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-3

Solving Linear Equations with the Variable on Both

Sides of the Equation

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-4

Equations with a Variable on Both Sides

1. Fractions: If the equation contains fractions, multiply both sides by the LCD to eliminate fractions.

2. Parentheses: Use the distributive property to remove parentheses.

3. Like Terms: Combine like terms on each side of the equation.

4. Addition property: Use the addition property to rewrite the equation with all terms containing the variable on one side of the equation and all terms not containing the variable on the other side of the equation.

5. Multiplication property: Use the multiplication property to isolate the variable.

6. Check: Check the solution in the original equation.

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-5

Solving Equations

4x + 6 = 2x + 4

4x – 2x + 6 = 2x – 2x + 4

2x + 6 = 4

2x + 6 – 6 = 4 – 6 (Subtract 6 from both sides)

2x = -2

2x = -2 (Divide both sides by 2) 2 2

x = -1

Example: Solve the equation 4x + 6 = 2x + 4

(Subtract 2x from both sides)

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-6

Solving Equations with Decimals

Example: Solve the equation 5.74x + 5.42 = 2.24x – 9.28

3.50x + 5.42 = – 9.28

x = -4.20

5.74x - 2.24x + 5.42 = 2.24x - 2.24x – 9.28 (Subtract 2.24x from both sides)

3.50x = -14.70

3.50x + 5.42 – 5.42 = – 9.28 – 5.42 (Subtract 5.42 from both sides)

3.50x = -14.70 (Divide both sides by 14)

3.5 3.5

Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 2-7

Identities and Contradictions

A conditional equation is true for a specific value or values of the variable.

An identity is true for all values of the variable. When we have an identity, we will state the solution is all real numbers.

A contradiction is not true for any value of the variable. When we have a contradiction, we will state that there is no solution.