1.3 Solving Linear Equations p. 19

What is an equation?
• A statement in which 2 expressions are =
Ex: Which of the following are equations?
a. 3x-7=12 b. 24x+5 c. 2x-7x 2 +4x 3 d. 12x+3= -4x-8

Properties of Equality
• Addition prop of = - can add the same term to both sides of an equation.
• Subtraction prop of = - can subtract the same term from both sides of an equation.
• Multiplication prop of = - can multiply both sides of an equation by the same term.
• Division prop of = - can divide both sides of an equation by the same term.
** So basically, whatever you do to one side of an equation, you MUST do to the other!

To solve an equation for a variable:
• Do order of operations backwards (undo
+/- first, then mult/div.)
• Keep going until the variable is by itself on one side of the equation
• You may have to simplify each side first.

Example: Solve for the variable.
2 x

8

16
9
2 x

8
9 x

8

9
2 x

36
5
 x

2

 
4

2 x

7

 x
5 x

10
 
8 x

28
 x
5 x

10
 
7 x

28
12 x

10
 
28
12 x
 
18 x
 
18
12 x
 
3
2

Ex: Solve for x.
2
3 x

1
5

2 x

3
10
30
2
3 x

1
5

30

2 x

3
10
20 x

6

60 x

9

40 x
 
15 x


15

40 x

3
8

40 x

6
 
9

Ex: Solve the equations.
5(x-4)=5x+12
5x-20=5x+12
-20=12
7x+14 -3x=4x+14
4x+14=4x+14
0=0
Doesn’t make sense!
Answer: No solution
This one makes sense, but there’s no variable left!
Answer: All real numbers

Dry ice is solid CO
2
. It does not melt, but changes into a gas at -109.3
o F. What is this temperature in o C?
Use F

9
5
C

32

109 .
3

9
5
C

32
5
9
(

141 .
3 )

C

141 .
3

9
5
C

78 .
5 o 
C

1.4 Rewriting Equations &
Formulas p. 26

Examples
• Solve 11x-9y= -4 for y.
-11x -11x
-9y=-11x-4
-9 -9 -9 y

11
9 x

9
4
• Solve 7x-3y=8 for x.
+3y +3y
7x=3y+8
7 7 7 x

3
7 y

8
7

Turn to page 28 in your book.
Know the Common
Formulas Chart on this page!

Ex: Solve the area of a trapezoid formula for b
1
.
A = ½ (b
1
+b
2
) h
2A = (b
1
+b
2
) h
2 A
 b
1
 b
2 h
2 A
 b
2 h
 b
1

Last Example:
• You are selling 2 types of hats: baseball hats & visors. Write an equation that represents total revenue.
Total
Revenue
Price of baseball cap
# of caps sold
Price of visor
# of visors sold
R = p
1
B + p
2
V