2.1
Equations, Formulas, and the
Problem-Solving Process
1. Verify solutions to equations.
2. Use formulas to solve problems.
What’s the difference?
x3
x3 5
Expression
Simplified
Equation
Solved
Equation: Two expressions set equal.
23 5
True
73 5
False
Solution: A number that makes an equation true
when it replaces the variable in the equation.
x  2 is the solution.
To Check a Possible Solution
 Replace the variable in the equation with the
value.
 If the resulting equation is true, the value is a
solution.
Solutions
Is a = 12 a solution?
Use parentheses!
4a  7  51
4
  7  51
412  7  51
48  7  51
55  51
NO
Solutions
6
Is x  a solution?
5
 8x  3  2x  15
6
6


 8   3  2   15
 5
 5
 48
12
3 
 15
5
5
 48 15 12 75



5
5
5
5
 63  63

5
5
Yes
Determine which of the following is a
solution for the equation.
6  x  4  2  4  x  3  6
a) –5
b) – 1
c) 2
d) 4
2.1
Determine which of the following is a
solution for the equation.
6  x  4  2  4  x  3  6
a) –5
b) – 1
c) 2
d) 4
2.1
Formula: An equation that describes a mathematical
relationship.
Perimeter:
Area:
The distance around a figure.
The total number of square units that fill a
figure.
Volume: The total number of cubic units that fill a
space.
Circumference:
Radius:
The distance around a circle.
The distance from the center of a circle to
any point on the circle.
Diameter: The distance across a circle through its
center.
Formulas
See page 95!!!!
Area:
A  lw
w
Perimeter: P  2l  2w
l
Area:
h
1
A  bh
2
b
Area:
r
A  r 2
Circumference:
C  2r
C  d
Formulas
Perimeter, Area or Volume?
Filling a pool with water?
Volume
Cover for a pool?
Area
Tile around a pool?
Perimeter
Fencing?
Perimeter
Laying carpet?
Area
Putting up a wallpaper
border?
Perimeter
Formulas
Suppose you have a rectangular pool that is 12 feet
wide and 20 feet long. The pool has a constant depth
of 4 feet. Find the perimeter, the area and the volume.
Perimeter:
P  2l  2w
P  220   212
P  40  24
P  64 feet
Formulas
Suppose you have a rectangular pool that is 12 feet
wide and 20 feet long. The pool has a constant
depth of 4 feet. Find the perimeter, the area and the
volume.
Area:
A  lw
A  20 12
A  240 square feet or ft2
Formulas
Suppose you have a rectangular pool that is 12
feet wide and 20 feet long. The pool has a
constant depth of 4 feet. Find the perimeter, the
area and the volume.
Volume: V  lwh
V  20 124 
V  960 cubic feet or ft3
A thermometer reads 30° C: what is this
temperature in degrees Fahrenheit?
9
F  C  32
5
a) 34F
b) 49F
c) 86F
d) 112F
2.1
A thermometer reads 30° C: what is this
temperature in degrees Fahrenheit?
9
F  C  32
5
a) 34F
b) 49F
c) 86F
d) 112F
2.1