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Equations as Balances
x 3  5
1 1 1
x
1
1 1 1
1
Take 3 away
from each side
1
x
1
 3]
x2
The golden rule of
solving equations
Whatever you do
to one side of the
equation, you must
do to the other.
1
The golden rule of
solving equations
x x 1
Whatever you do
to one side of the
equation, you must
do to the other.
This means that we
have taken 1 away
from each side.
1
2x  1  7
1
1 1
1 1 1
x x
 1]
2x  6
1 1 1
x
 2]
1
1 1
1 1
x 3
1
1
x x 1
x
1 1
1 1
2x  1  x  6
 x]
x 1  6
 1]
x 5
Solving Equations Showing Good Working
x  5  12
5x  3  33
 3]
5x  30
 5]
x6
 5]
3  5 x
 x]
3 x  5
 3]
x2
x  17
5x  8
 5]
x  85
Equation
To understand what
comes later, let’s show it
Reversing The Flow Chart
to Solve the Equation
as a Flow Chart
x
4
7
x  3  8
x
x
2x  6  40 x
4
3
2
7
 4 x  28
7
8
 3 x  5
8
2x
6
2

6
x  17
34
40 40
What it means
5x  4  8
x
3( x  4)  27 x
x
4
5  3 x
5
4
4
5x
4
How we will solve
8
 4 12  5 x  12
5
8
4
 3 27

3
9
x4
27
x
4
5
3
x 5
 5  2  4 x  8
3
Example
1
x x 1
1
x
1 1
1 1
2x  1  x  6
 x]
 1]
2x  x  1  x  x  6
x 1  6
x  1 1  6 1
x 5
Example
x
x x x
x x 1
x 1 x
1 x
1 1
1 1 1
6x 1  3x  7
 3x] 6x  3x 1  3x  3x  7
 1]
 3]
3x 1 1  7 1
3x 2

3 3
3x  1  7
3x  6
x2
More examples
7 x  6  4x  12
5x  3  2 x  5
 2x]
3x  3  5
 4x]
3x  6  12
 3]
3x  2
 6]
3x  18
 3]
x
 3]
x6
2
3
3x 1  5x 11
 3x]
1  2x 11
 11]
10  2x
 2]
5 x