The Balancing Method for Solving Equations
Example
x
x
3
2x + 3 = 11
2x + 3 – 3 = 11 – 3
11
x
x
2x = 8
2x = 8
2
2
x = 4
8
x
4
Exercise 1
Solve the following equations using the Bar Method, showing the balancing
method alongside.
1.
a
a
a
10
19
2.
b
b
5
9
3.
c
c
c
c
1
9
4.
d
d
d
2
11
5.
e
e
6.
e
f
e
35
f
e
5
f
7
25
7.
g
g
4
9
8.
h
h
h
h
14
2
Exercise 2
Solve the following equations using the Bar Method, showing the balancing
method alongside.
1.
3a + 1 = 10
2.
2b + 7 = 13
3.
5c + 5 = 30
4.
4d + 7 = 15
5.
8e + 3 = 19
6.
6f + 1 = 13
7.
9g + 11 = 110
8.
5h + 9 = 34
9.
2i + 15 = 20
10.
3j + 5 = 13
Exercise 3
Solve the following equations using the balancing method alongside.
1.
3a + 5 = 17
2.
2b + 5 = 17
3.
2c - 5 = 3
4.
5d + 3 = 18
5.
3e - 5 = 19
6.
6f + 1 = 13
7.
7g + 5 = 40
8.
3h - 20 = 40
9.
4i + 22 = 26
10.
6j - 5 = 11
Solving Equations using the Bar Method
Example 1
x
x
12
20
x
x
8
x
4
Exercise 1
Solve the following equations using the Bar Method:
1.
a
a
a
19
2.
b
b
10
8
12
3.
c
c
c
c
3
15
4.
d
d
d
10
25
5.
e
e
6.
e
f
e
27
e
f
7
f
1
10
7.
g
g
5
10
8.
h
h
h
h
10
4
Exercise 2
Solve the following equations using the Bar Method.
1.
2a + 3 = 13
2.
3b + 1 = 16
3.
4c + 3 = 23
4.
5d + 4 = 24
5.
7e + 2 = 37
6.
2f + 20 = 44
7.
6g + 3 = 21
8.
10h + 3 = 33
9.
2i + 7 = 10
10.
5j + 3 = 5
The Bar Method for Solving Equations with unknowns on both sides
Example
x
x
x
x
x
7
3x + 7 = x + 13
3x + 7 – x = x + 13 - x
13
x
7
2x + 7 = 13
13
x
2x + 7- 7 = 13 -7
x
6
2x = 6
2
2
x = 3
x
3
Exercise 1
Solve the following equations using the Bar Method, showing the balancing
method alongside.
1.
a
a
a
5
a
a
23
2.
b
b
3.
c
c
d
2
8
e
e
5
11
f
h
h
9
17
e
e
f
f
h
h
c
d
d
e
e
6.
7.
c
d
d
e
e
3
11
c
c
4.
5.
b
f
9
h
1
h
3
11
Exercise 2
Solve the following equations using the Bar Method, showing the balancing
method alongside.
1.
5a + 1 = 2a + 7
2.
7b - 3 = 2b + 17
3.
9c + 5 = 3c + 35
4.
4d - 11 = 2d + 15
5.
8e + 3 = e + 52
6.
6f - 11 = 4f + 10
7.
7g + 100 = 2g + 20
8.
6h + 2 = 3h - 13
9.
9i + 15 = i + 20
10.
3j + 3 = 15 -3j
Exercise 3
Solve the following equations using the balancing method.
1.
7a + 3 = 3a + 31
2.
5b - 3 = b + 17
3.
8c + 3 = 3c + 43
4.
3d + 3 = 18 – 2d
5.
9e + 1 = 5e + 29
6.
6f + 30 = 4f + 10
7.
11g + 3 = 21 - g
8.
7h + 12 = 2h - 13
9.
8i + 15 = 2i + 51
10.
5j + 3 = 15 -5j