1. 8
Chapter
Chapter 2
Introduction to Algebra

2. Solving Equations: Using the Addition and Multiplication Properties
Section
8.4
Solving Equations: Using the Addition and Multiplication Properties

3. Solve Equations Using Addition and Multiplication Properties.
Objective A
Solve Equations Using Addition and Multiplication Properties.

4. Steps for Solving an Equation
Step 1: If parentheses are present, use the distributive property.
Step 2: Combine any like terms on each side of the equation.
Step 3: Use the addition property of equality to rewrite the equation so that variable terms are on one side of the equation and constant terms are on the other side.
Step 4: Use the multiplication property of equality to divide both sides by the numerical coefficient of the variable to solve for.
Step 5: Check the solution in the original equation.
Objective A

5. Example
Solve 3x – 12 = 24
Check:
Objective A

6. Example
Solve: 17 – x + 3 = 15 – (–6)
Objective A

7. Example
Solve:
Objective A

8. Example
Solve: 7x = 4x – 1.6
Objective A

9. Solve Equations Containing Parenthesis.
Objective B
Solve Equations Containing Parenthesis.

10. Example
Solve: 7(x – 3) = 9x – 8
Objective A

11. Write Numerical Sentences as Equations.
Objective C
Write Numerical Sentences as Equations.

12. Writing Sentences as Equations
Key Words or Phrases
Examples
Symbols
equals
3 equals 2 plus 1
3 = 2 + 1
gives
the quotient of 10 and –5 gives –2
is/was
17 minus 12 is 5
17 – 12 = 5
yields
11 plus 2 yields 13
= 13
amounts to
twice –15 amounts to –30
2(–15) = –30
is equal to
–24 is equal to 2 times
–12
–24 = 2(–12)
Objective A

13. Example Translate each sentence into an equation.
a. The product of 7 and 6 is 42.
7(6) = 42
b. Twice the sum of 3 and 5 is equal to 16.
2(3 + 5) = 16
Objective A