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Algebra 1
Section 2.6
Simplifying Equations
You can use the distributive
property to:
Remove parentheses
Combine like terms
Example 1
Solve 3x + 2 + 5x – 7 = 28.
8x – 5 = 28
8x – 5 + 5 = 28 + 5
8x = 33
Example 1
8x = 33
8x 33
=
8
8
33
x=
8
Did you check your answer?
Example 2
Solve 3(x + 1) – (x – 2) = 13.
3x + 3 – x + 2 = 13
2x + 5 = 13
2x = 8
x=4
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
Example 3
x = 11
x = John’s age
John is 11 years old
4x = John’s mother’s age
John’s mother is 44 years old
2x = John’s brother’s age
John’s brother is 22 years old
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.
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.
Converting a Repeating Decimal to
a Fraction of Two Integers
4. Solve the resulting equation
and reduce the fraction to
lowest terms.
Example 4
Express 0.36 as a quotient of
integers.
x = 0.36
100x = 36.36
–
99x = 36
Example 4
Express 0.36 as a quotient of
integers.
99x = 36
99x 36
=
99
99
36
4
x=
99
11
Example 5
Express 1.36 as a quotient of
integers.
x = 1.36
10x = 13.66
–
9x = 12.3
Example 5
Express 1.36 as a quotient of
integers.
9x = 12.3
9x 12.3
=
9
9
12.3
123
41
x=
30
90
9
Homework:
pp. 77-78