Solving One Step Equation

1
Solving One-Step Equations
An equation consists of 3 parts.
Expression
Expression

(Left)
(Right)
x 1
6
x 1
6
2
A Two-pan Balance
Scientists often use a two-pan balance to weigh
objects by placing an object of unknown weight on
one pan and known weights on the other pan.
3
A Two-pan Balance
When the two sides are balanced, the unknown
weight is equal to the known weight on the other
pan.
4
In the diagram below, how much does object a
weigh?
Example 1
Since the two sides are balanced, object a
weighs 5 ounces.
5
Example 2
How much does object x weigh?
In order to determine the weight of object x,
we need to see how many one-ounce weights balance
object x by itself.
6
Example 2
How much does object x weigh?
Take the one ounce weight off the left-hand side
of the two-pan balance, leaving object x by
itself.
7
Example 2
How much does object x weigh?
Take the one ounce weight off the left hand side
of the two-pan balance, leaving object x by
itself.
8
Example 2
How much does object x weigh?
The balance will tip to the right.
9
Example 2
How much does object x weigh?
In order to return the balance to equilibrium, we
must take a one-ounce weight off the right-hand
side of the balance as well.
10
Example 2
How much does object x weigh?
In order to return the balance to equilibrium, we
must take a one-ounce weight off the right-hand
side of the balance as well.
11
Example 2
How much does object x weigh?
Now, object x must weigh 5 ounces.
12
An equation is like a two-pan balance.
Right Expression
Left Expression

13
Solving One-Step Equations
x 1
6
x 1 6

14
Solving One-Step Equations
x 1 6


0
Diagram 1 Equilibrium
15
Solving One-Step Equations
x 1 6

16
Solving One-Step Equations
x 1 6

Diagram 2 Disequilibrium
17
Solving One-Step Equations
x 1 6

18
Solving One-Step Equations
x 1 6

Diagram 3 Equilibrium
19
Solving One-Step Equations
x 1 6

x 5
Diagram 4 Equilibrium Variable Isolated
20
Example 1
6 x 2
Steps

1) Add (-2) to right side.
Diagram 1 Equilibrium
21
Example 1
6 x 2
Steps

1) Add (-2) to right side.
2) Add (-2) to left side.
Diagram 2 Disequilibrium
22
Example 1
6 x 2
Steps

1) Add (-2) to right side.
x 0
2) Add (-2) to left side.
Diagram 3 Equilibrium
23
Example 1
6 x 2
Diagram 4 Equilibrium Variable Isolated
Steps

1) Add (-2) to right side.
4
x 0
2) Add (-2) to left side.
4 x
24
Example 2
t (-2) 6
Steps

1) Add (2) to left side.
2) Add (2) to right side.
25
Example 2
t (-2) 6
Steps

1) Add (2) to left side.
t 0
8
2) Add (2) to right side.
t 8
26
Tonights Homework
Solve the following equations using the two-pan
balance model. For each equation draw a diagram
of the two-pan balance and list the steps.
1) a 4 9
2) y (-2) 8
27
Western Division Champions 2006