Download Chapter Two 2.1

Section 2.1
Introduction to
Equations
Copyright © 2013 Pearson Education, Inc.
Page 91
What is the difference between an equation and an
expression?
• Not the same
• Only an Equation has an equal sign
• Simplify an expression (1.8)
• Solve an equation
Page 91
Example
Solve each equation.
a. x + 21 = 9
b. n – 8 = 17
Solution
a. x + 21 = 9
b.
x + 21 + (−21) = 9 + (−21)
Page 92
n – 8 = 17
n – 8 + 8 = 17 + 8
x + 0 = −12
n + 0 = 25
x = −12
n = 25
The solution is −12.
The solution is 25.
Example
Page 93
Solve the equation −7 + x = 12 and then check the
solution.
Solution
Isolate x by adding 7 to each side.
−7 + x = 12
−7 + 7 + x = 12 + 7
0 + x = 19
x = 19
The solution is 19.
Check:
−7 + x = 12
?
−7 + 19 = 12
12 = 12
The answer checks.
Page 94
Example
Page 95
Solve each equation.
a. 1 x  8
b. −11a = 33
Solution
1
a.
x 8
b.
6
6
1
6 x  86
6
1 x  48
x  48
The solution is 48.
−11a = 33
11a
33

11 11
a  3
The solution is −3.
Example
Page 95
2
2
Solve the equation   x and then check the solution.
5
9
Solution
2
2
 x
5
9
9 2
2  9
       x
2 5
9  2
9
  1 x
5
9
 x
5
Check: 2   2 x
9
The solution is  .
5
5
9
2
2 9
   
5
9 5
2 2

5 5
The answer checks.
Example
Page 96
A veterinary assistant holds a cat and steps on a scale.
The scale reads 153 lbs. Alone the assistant weighs 146
lbs.
a. Write a formula to show the relationship of the weight
of the cat, x, and the assistant.
b. Determine how much the cat weighs.
Solution
b.
146 + x = 153
a. 146 + x = 153
146 + (−146) + x = 153 − 146
x=7
The cat weighs 7 lbs.
Example
Page 96
In recent years, many of Alaska’s major glaciers have
been melting at a rate of 24 cubic miles per year.
a. Write a formula that gives the cubic miles of ice I that
will melt in x years.
b. At this rate, determine how long it will take for 300
cubic miles of ice to melt.
Solution
b. I  24 x
a. I = 24x
300  24 x
It will take 12.5 years for
300 miles of ice to melt.
300 24 x

24
24
12.5  x
End of chapter problems
•
do 24, 46, 48 on page 98-99
•
do 63, 64 on page 98-99
DONE
Objectives
•
Basic Concepts
•
Equations and Solutions
•
The Addition Property of Equality
•
The Multiplication Property of Equality