Chapter 9 - XYZ Custom Plus

Introduction . . .
The Addition Property of Equality
Previously we defined complementary angles as two angles whose sum is 90°. If
A and B are complementary angles, then
9.2
Objectives
A Identify a solution to an equation.
b u se the addition property of
equality to solve linear equations.
A 1 B 5 90°
A
B
Examples now playing at
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Complementary angles
If we know that A 5 30°, then we can substitute 30° for A in the formula above to
obtain the equation
30° 1 B 5 90°
In this section we will learn how to solve equations like this one that involve addition
and subtraction with one variable.
In general, solving an equation involves finding all replacements for the variable
that make the equation a true statement.
A
Solutions to Equations
Definition
A solution for an equation is a number that when used in place of the
variable makes the equation a true statement.
For example, the equation x 1 3 5 7 has as its solution the number 4, because
replacing x
with 4 in the equation gives a true statement:
ExAmplE 1
SOlutiOn
result is a true statement:
When x 5 4
the equation x 1 3 5 7
becomes 4 1 3 5 7
or 7 5 7 A true statement
Is x 5 5 the solution to the equation 3x
1 2 5 17?
To see if it is, we replace x
with 5 in the equation and find out if the
the equation
When x 5 5
3x
1 2 5 17
becomes 3(5) 1 2 5 17
15 1 2 5 17
17 5 17 A true statement
Because the result is a true statement, we can conclude that x 5 5 is the solution
to 3x
1 2 5 17.
Note
Although an equation
may have many solutions,
the equations
we work with in the first part
of this chapter will always have a
single solution.
prACtiCE prOblEmS
1. Show that x 5 3 is the solution
to the equation 5x
2 4 5 11.
Answer
1. See solutions section.
9.2 The Addition Property of Equality
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