Download Section 2.1

Section 2.1
Solving Equations Using
Properties of Equality
Objectives
Determine whether a number is a solution
 Use the addition property of equality
 Use the subtraction property of equality
 Use the multiplication property of equality
 Use the division property of equality

Objective 1: Determine Whether a Number
is a Solution

An equation is a statement indicating that two
expressions are equal, for example:





x + 5 = 15
x + 5 is the left side
15 is the right side
A number that makes an equation true when
substituted for the variable is called a
solution and it is said to satisfy the equation.
The solution set of an equation is the set of
all numbers that make the equation true.
EXAMPLE 1
Check to determine whether 9 is a
solution of 3y – 1 = 2y + 7?
Objective 2: Use the Addition Property of
Equality



To solve an equation means to find all values
of the variable that make the equation true.
Equations with the same solutions are called
equivalent expressions.
Addition property of equality: Adding the
same number to both sides of an equation does
not change its solution.
 For
any real numbers a, b, and c,
if a = b, then a + c = b + c
EXAMPLE 2
Solve: x – 2 = 3
Objective 3: Use the Subtraction Property
of Equality


Since any subtraction can be written as an
addition by adding the opposite of the number to
be subtracted, this property is an extension of
the addition property of equality.
Subtraction property of equality: Subtracting
the same number from both sides of an equation
does not change its solution.
 For
any real numbers a, b, and c,
if a = b, then a – c = b – c
EXAMPLE 4
Solve:
a. x + 1/8 = 7/4
b. 54.9 + x = 45.2
Objective 4: Use the Multiplication
Property of Equality

Multiplication property of equality:
Multiplying both sides of an equation by
the same nonzero number does not
change its solution.
 For
any real numbers a, b, and c, where c is
not 0, if a = b, then ca = cb
EXAMPLE 5
𝑥
3
Solve: = 25
Objective 5: Use the Division Property of
Equality

Division property of equality: Dividing
both sides of an equation by the same
nonzero number does not change its
solution.
 For
any real numbers a, b, and c, where c is
not 0, if a = b, then a/c = b/c
EXAMPLE 7
Solve:
a. 2t = 80
b. –6.02 = –8.6t