1. Algebra 1
Section 2.6

2. Simplifying Equations
You can use the distributive property to:
Remove parentheses
Combine like terms

3. Example 1 Solve 3x + 2 + 5x – 7 = 28. 8x – 5 = 28 8x – 5 + 5 = 28 + 5

4. Did you check your answer?
Example 1
8x = 33 8x 8 = 33 33 8
x =
Did you check your answer?

5. Example 2 Solve 3(x + 1) – (x – 2) = 13. 3x + 3 – x + 2 = 13

6. Example 3 Let x = John’s age Let 4x = John’s mother’s age
Let 2x = John’s brother’s age
4x + 2x + x + 3 = 80
7x + 3 = 80
x = 11

7. Example 3 x = 11 x = John’s age 4x = John’s mother’s age
2x = John’s brother’s age
John is 11 years old
John’s mother is 44 years old
John’s brother is 22 years old

8. Converting a Repeating Decimal to a Fraction of Two Integers
1. Write an equation in which x is equal to the repeating decimal.
2. Use the Multiplication Property of Equality to multiply both sides of this equation by 10n, where n is the number of repeating digits.

9. Converting a Repeating Decimal to a Fraction of Two Integers
3. Subtract the original equation from the new equation formed by the multiplication. This step is an application of the Addition Property of Equality since we are subtracting equal quantities from each side of the equation.

10. Converting a Repeating Decimal to a Fraction of Two Integers
4. Solve the resulting equation and reduce the fraction to lowest terms.

11. Example 4 Express 0.36 as a quotient of integers. x = 0.36–
99x = 36

12. Example 4 Express 0.36 as a quotient of integers. 99x = 36 99x 99 = 3611
x = 36 99
x =

13. Example 5 Express 1.36 as a quotient of integers. x = 1.36 10x = 13.66–
9x = 12.3

14. Example 5 Express 1.36 as a quotient of integers. 9x = 12.3 9x 9 =
123 90
x = 41 30
x =
12.3 9
x =

15. Homework: pp