Fundamentals of Mathematics, 2008a

641
11.3.3.1 Exercises for Review
Exercise 11.3.26 (Solution on p. 683.)
(Section 4.3) Convert 24
11
to a mixed number
Exercise 11.3.27
3
(Section 4.4) Determine the missing numerator:
8 = ?
64 .
Exercise 11.3.28 (Solution on p. 684.)
(Section 5.6) Simplify 5 6 − 1 4
1 .
12
Exercise 11.3.29
(Section 7.5) Convert 5
16
to a percent.
Exercise 11.3.30 (Solution on p. 684.)
(Section 11.2) In the expression 6k, how many k's are there?
11.4 Solving Equations of the Form x+a=b and x-a=b 4
11.4.1 Section Overview
• Equations
• Solutions and Equivalent Equations
• Solving Equations
11.4.2 Equations
Equation
An equation is a statement that two algebraic expressions are equal.
The following are examples of equations:
x + 6 =
[U+FE38]
This
expression =
10
}{{}
This
expression
x − 4 =
} {{ }
This
expression =
−11
}{{}
This
expression
3y − 5 =
} {{ }
This
expression
=
−2 + 2y
} {{ }
This
expression
Notice that x + 6, x − 4, and 3y − 5 are not equations. They are expressions. They are not equations because
there is no statement that each of these expressions is equal to another expression.
11.4.3 Solutions and Equivalent Equations
Conditional Equations
The truth of some equations is conditional upon the value chosen for the variable. Such equations are called
conditional equations. There are two additional types of equations. They are examined in courses in
algebra, so we will not consider them now.
Solutions and Solving an Equation
The set of values that, when substituted for the variables, make the equation true, are called the solutions
of the equation.
An equation has been solved when all its solutions have been found.
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