Transpose Method – Solve Linear Equations

Solve the following equations and check answers:

1. x + 4 = 9

Solution: Given x + 4 = 9

Transposing 4 to right hand side we get,

x = 9 – 4

x = 5

Check: Substituting x = 5 in LHS, we get,

LHS = x + 4

= 5 + 4

= 9

RHS = 9

LHS = RHS

Hence, Checked.

2. x – 2 = 8

Solution: Given x – 2 = 8

Transposing 2 to right hand side we get,

x = 8 + 2

x = 10
Check: Substituting x = 10 in LHS,

we get, LHS = x – 2

= 10 – 2

= 8

RHS = 8

LHS = RHS

Hence, Checked.

3. 4x = 36

Solution: Given 4x = 36

Transposing 4 to right hand side we get,

x = 36/4

x = 9

Check: Substituting x = 9 in LHS,

we get, LHS = 4x

= 4 x 9

= 36

RHS = 36

LHS = RHS

Hence, Checked.

4. x/2 = 20

x = 20 x 2

x = 40

Check: Substituting x = 40 in LHS,

we get, LHS = 40/2

= 20

LHS = 20

RHS = 20

LHS = RHS

Hence, Checked.

5. 5x – 3 = 3x + 7

Transposing 3x on left hand side

5x – 3 – 3x = 7

Transposing 3 on right hand side

5x – 3x = 7 + 3

2x = 10

x =10/2

x = 5

Check: Substituting x = 5 in LHS,

we get, LHS = 5x – 3

= 5 x 5 – 3

= 25 – 3

= 22

LHS = 22

RHS = 3x + 7

= 3 x 5 + 7

=15 + 7

= 22

LHS = RHS

Hence, Checked.

6. (4/5) + x = (7/5)

Transposing 4/5 on right hand side

x = 7/5 – 4/5

x = (7 – 4)/5

= 3/5

x = 3/5 Check: Substituting x = 3/5 in LHS,

we get, LHS = 4/5 + x

= 4/5 + 3/5

= 7/5

LHS = 7/5

RHS = 7/5

LHS = RHS

Hence, Checked.

7. 2x – 4 = 8

2x = 8 + 4

2x = 12

x = 12/2

x = 6

5x + 3 = 2x + 12

Transpose 2x to LHS

5x + 3 – 2x = 12

3x = 12 -3

= 9

3x = 9

x = 9/3

x = 3

∴LHS = RHS

8. 5(2x- 3) – 2(3x – 4) = 9

Simplify brackets we get

10x – 15 – 6x + 8 = 9

10x – 6x – 15 + 8 = 9

4x – 7 = 9

Transpose 7 on right hand side

4x = 7 + 9

4x = 16

x = 16/4

x= 4

Check: Substituting x = 4 in LHS,

we get, LHS = 5(2x – 3) – 2(3x – 4)

= 5(2 x 4 – 3) – 2(3 x 4 – 4)

= 5(8 – 3) – 2(12 – 4)

= 5(5) – 2(8)

= 25 – 16

= 9

LHS = 9

RHS = 9

LHS = RHS

Hence, Checked.